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1
Attia, Hazem Ali. "Dynamic model of multi-rigid-body systems based on particle dynamics with recursive approach." Journal of Applied Mathematics 2005, no. 4 (2005): 365–82. http://dx.doi.org/10.1155/jam.2005.365.
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A dynamic model for multi-rigid-body systems which consists of interconnected rigid bodies based on particle dynamics and a recursive approach is presented. The method uses the concepts of linear and angular momentums to generate the rigid body equations of motion in terms of the Cartesian coordinates of a dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotational transformation matrix. For the open-chain system, the equations of motion are generated recursively along the serial chains. A closed-chain system is transformed to open-chain by cutting suitable kinematical joints and introducing cut-joint constraints. An example is chosen to demonstrate the generality and simplicity of the developed formulation.
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Leshchenko, D., and T. Kozachenko. "PROBLEMS OF EVOLUTION OF RIGID BODY MOTION SIMILAR TO LAGRANGE TOP." Mechanics And Mathematical Methods 4, no. 1 (2022): 23–31. http://dx.doi.org/10.31650/2618-0650-2022-4-1-23-31.
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The problem of evolution of the rigid body rotations about a fixed point continues to attract the attention of researches. In many cases, the motion in the Lagrange case can be regarded as a generating motion of the rigid body. In this case the body is assumed to have a fixed point and to be in the gravitational field, with the center of mass of the body and the fixed point both lying on the dynamic symmetry axes of the body. A restoring torque, analogues to the moment of the gravity forces, is created by the aerodynamic forces acting on the body in the gas flow. Therefore, the motions, close to the Lagrange case, have been investigated in a number of works on the aircraft dynamics, where various perturbation torques were taken into account in addition to the restoring torque. Many works have studied the rotational motion of a heavy rigid body about a fixed point under the action of perturbation and restoring torques. The correction of the studied models is carried out by taking into account external and internal perturbation factors of various physical nature as well as relevant assumptions according to unperturbed motion. The results of reviewed works may be of interest to specialists in the field of rigid body dynamics, gyroscopy, and applications of asymptotic methods. The authors of this papers present a new approach for the investigation of perturbed motions of Lagrange top for perturbations which assumes averaging with respect to the phase of the nutation angle. Nonlinear equations of motions are simplified and solved explicitly, so that the description of motion is obtained. Asymptotic approach permits to obtain some qualitative results and to describe evolution of rigid body motion using simplified averaged equations. Thus it is possible to avoid numerical integration. The authors present a unified approach to the dynamics of angular motions of rigid bodies subject to perturbation torques of different physical nature. These papers contains both the basic foundations of the rigid body dynamics and the application of the asymptotic method of averaging. The approach based on the averaging procedure is applicable to rigid bodies closed to Lagrange gyroscope. The presented brief survey does not purport to be complete and can be expanded. However, it is clear from this survey that there is an literature on the dynamics of rigid body moving about a fixed point under the influence of perturbation torques of various physical nature. The research in this area is in connection with the problems of motion of flying vehicles, gyroscopes, and other objects of modern technology
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Leshchenko, D., and T. Kozachenko. "SOME PROBLEMS ABOUT THE MOTION OF A RIGID BODY IN A RESISTIVE MEDIUM." Mechanics And Mathematical Methods 3, no. 2 (2021): 6–17. http://dx.doi.org/10.31650/2618-0650-2021-3-2-6-17.
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The dynamics of rotating rigid bodies is a classical topic of study in mechanics. In the eighteenth and nineteenth centuries, several aspects of a rotating rigid body motion were studied by famous mathematicians as Euler, Jacobi, Poinsot, Lagrange, and Kovalevskya. However, the study of the dynamics of rotating bodies of still important for aplications such as the dynamics of satellite-gyrostat, spacecraft, re-entry vehicles, theory of gyroscopes, modern technology, navigation, space engineering and many other areas. A number of studies are devoted to the dynamics of a rigid body in a resistive medium. The presence of the velocity of proper rotation of the rigid body leads to the apearance of dissipative torques causing the braking of the body rotation. These torques depend on the properties of resistant medium in which the rigid body motions occur, on the body shape, on the properties of the surface of the rigid body and the distribution of mass in the body and on the characters of the rigid body motion. Therefore, the dependence of the resistant torque on the orientation of the rigid body and its angular velocity can de quite complicated and requires consideration of the motion of the medium around the body in the general case. We confine ourselves in this paper to some simple relations that can qualitative describe the resistance to rigid body rotation at small angular velocities and are used in the literature. In setting up the equations of motion of a rigid body moving in viscous medium, we need to consider the nature of the resisting force generated by the motion of the rigid body. The evolution of rotations of a rigid body influenced by dissipative disturbing torques were studied in many papers and books. The problems of motion of a rigid body about fixed point in a resistive medium described by nonlinear dynamic Euler equations. An analytical solution of the problem when the torques of external resistance forces are proportional to the corresponding projections of the angular velocity of the rigid body is obtain in several works. The dependence of the dissipative torque of the resistant forces on the angular velocity vector of rotation of the rigid body is assumed to be linear. We consider dynamics of a rigid body with arbitrary moments of inertia subjected to external torques include small dissipative torques.
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Leshchenko, D., and T. Kozachenko. "EVOLUTION OF ROTATIONAL MOTIONS IN A RESISTIVE MEDIUM OF A NEARLY DYNAMICALLY SPHERICAL GYROSTAT SUBJECTED TO CONSTANT BODY-FIXED TORQUES." Mechanics And Mathematical Methods 4, no. 2 (2022): 19–31. http://dx.doi.org/10.31650/2618-0650-2022-4-2-19-31.
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A satellite or a spacecraft in its motion about the center of mass is affected by the torques of forces of various physical nature. It is influenced by the gravitational, aerodynamic torques, the torques due to the light pressure, and the torques due to the motions of masses inside the body. These motions may have various causes, for example, the presence of fluid in the cavities in the body (for example, liquid fuel or oxidizer in the tanks of a rocket). Therefore, there is a necessity to study the problems of the dynamics of bodies with cavities containing a viscous fluid, to calculate the motion of spacecrafts about the center of mass, as well as their orientation and stabilization. The mentioned torques, acting on the body, are often relatively small and can be considered as perturbations. It is natural to use the methods of small parameter to analyze the dynamics of rigid body under the action of applied torques. The method applied in this paper is the Krylov-Bogolubov asymptotic averaging method. The studies of F. L. Chernousko showed that solving the problems of dynamics of a rigid body with a viscous fluid can be subdivided into two parts – the hydrodynamic and dynamic ones – which can greatly simplify the initial problem. We investigated the motion about its center of mass in a resistive medium of a nearly dynamically spherical rigid body with a cavity filled with a viscous fluid at small Reynolds numbers, subjected to constant body-fixed torque which is described by the system of differential equations, considering the asymptotic approximation of the moments of the viscous fluid in the cavity. The determination of the motions of forces acting on the body from side of the viscous fluid in the cavity was proposed in the works of F. L. Chernousko. We obtained the system of equations of motion in the standard form which refined in square-approximation by small parameter. The Cauchy problem for a system determined after averaging was analyzed. The evolution of the motion of a rigid body under the action of small internal and external torques of forces is described by the solutions which obtained as a result of asymptotic, analytical and numerical calculations over an infinite time interval.
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Udwadia, Firdaus E., and Aaron D. Schutte. "A unified approach to rigid body rotational dynamics and control." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2138 (2011): 395–414. http://dx.doi.org/10.1098/rspa.2011.0233.
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This paper develops a unified methodology for obtaining both the general equations of motion describing the rotational dynamics of a rigid body using quaternions as well as its control. This is achieved in a simple systematic manner using the so-called fundamental equation of constrained motion that permits both the dynamics and the control to be placed within a common framework. It is shown that a first application of this equation yields, in closed form, the equations of rotational dynamics, whereas a second application of the self-same equation yields two new methods for explicitly determining, in closed form, the nonlinear control torque needed to change the orientation of a rigid body. The stability of the controllers developed is analysed, and numerical examples showing the ease and efficacy of the unified methodology are provided.
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O’Reilly, O. M. "On the Computation of Relative Rotations and Geometric Phases in the Motions of Rigid Bodies." Journal of Applied Mechanics 64, no. 4 (1997): 969–74. http://dx.doi.org/10.1115/1.2789008.
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In this paper, expressions are established for certain relative rotations which arise in motions of rigid bodies. A comparison of these results with existing relations for geometric phases in the motions of rigid bodies provides alternative expressions of, and computational methods for, the relative rotation. The computational aspects are illustrated using several examples from rigid-body dynamics: namely, the moment-free motion of a rigid body, rolling disks, and sliding disks.
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Choi, K.-B. "Dynamics of a compliant mechanism based on flexure hinges." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 219, no. 2 (2005): 225–35. http://dx.doi.org/10.1243/095440605x8478.
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This paper presents a novel equation of motion for flexure hinge-based mechanisms. The conventional equation of motion presented in previous work does not adequately describe the behaviours of rigid bodies for the following reasons: firstly, rotational directions for a transformed stiffness lack consistency at the two ends of a flexure hinge; secondly, the length of the flexure hinge is not considered in the equation. The equation of motion proposed in this study solves these problems. Modal analyses are carried out using the proposed equation of motion, the conventional equation of motion found in previous work, and a finite element method. The results show that the proposed equation of motion describes the behaviours of the rigid bodies better than the conventional equation of motion does.
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Dai, Bing, Guang Bin Yu, Jun Peng Shao, and Long Huang. "Eccentricity and Rotational Speed Effect on the Rotor-Bearing." Applied Mechanics and Materials 274 (January 2013): 237–40. http://dx.doi.org/10.4028/www.scientific.net/amm.274.237.
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Bearing dimensionless nonlinear oil film force model is deduced based on Capone theory of cylindrical bearings in this paper. Jeffcot rigid rotor-bearing system dynamic equations are built based on nonlinear dynamics, bifurcation, chaos theory. Eccentricity increases with the speed of the system by writing MATLAB codes. It appears the periodic motion, times of periodic motion and a series of non-linear kinetics. The system eccentricity increases with a series of emergence of non-linear dynamics when speed conditions is fixed, which is the actual system design’s basis. The finite element model of gas turbine rotor-bearing system is built by ANSYS software platform in this paper. The radial bearing deformation relationship are obtained by deformation theory of centrifugal force at high speed bearing radial deformation.
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GUPTA, SHUCHI, KEYA DHARAMVIR, and V. K. JINDAL. "STRUCTURE AND DYNAMICS OF CARBON NANOTUBES IN CONTACT WITH GRAPHITE SURFACE AND OTHER CONCENTRIC NANOTUBES." International Journal of Modern Physics B 18, no. 07 (2004): 1021–41. http://dx.doi.org/10.1142/s0217979204024513.
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Rigid carbon nanotubes in single and double walled formations, placed on a graphite surface, are bounced, rotated, slid and rolled. Various features associated with these motions are studied by assuming a 6-exp form of interaction (Van der Waal's attraction and Born–Mayer repulsion) among the C-atoms. Calculations reported here are for tubes of diameter around 14 Å, for which rigid tube approximation is known to work well. The oscillatory motion corresponding to rolling has the softest mode, whereas the one with highest frequency corresponds to bouncing. The energy barriers corresponding to these motions are also reported in this paper. The rotational and translational energy barriers for the movement of one nanotube with respect to the other one, in a double walled nanotube, have also been studied and it turns out that these tubes rotate and slide freely at room temperature. The translational energy barrier, in case of zigzag tubes, is interestingly, an order of magnitude higher than that of armchair tubes. In case of rotation, the case is reverse. Furthermore, it turns out that any drag of a concentric nanotube along the long axis direction is coupled with rotation, indicating easy screw motion instead of a simple drag. We also describe the dynamics of translational telescopic motion of a multiwalled nanotube assembly where a core oscillates within an open ended outer shell assembly.
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Liu, Zhan Fang, and Xiao Wei Guo. "Dynamical Analysis on a Mass at the Tip of a Flexible Rod on a Rotating Base." Applied Mechanics and Materials 105-107 (September 2011): 536–40. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.536.
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Abstract: A dynamical analysis on a mass fixed at the tip of a massless flexible rod mounting on a rotating rigid body is presented in which the motion of the mass is kept in the plane of rotation as small deformation of the rod is assumed. For the rigid body undergoing a constant angular velocity the centrifugal forces and Coriolis force on the mass are considered. There exist two dynamic frequencies in which the first order dynamic frequency decreases with rotational velocity up to zero that is associated with a limit rotational velocity of the system. The motion trajectories of the mass in the rotational plane at different rotational velocities exhibit multiple traces with respect to the conventional line trace and may be split into the non-eccentric and eccentric portions. With a view on the change of amplitudes a critical rotational velocity is discussed.
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Richard, M. J., I. Bindzi, and C. M. Gosselin. "A Topological Approach to the Dynamic Simulation of Articulated Machinery." Journal of Mechanical Design 117, no. 1 (1995): 199–202. http://dx.doi.org/10.1115/1.2826107.
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This article presents a method for deriving the equations describing the motion of tree-structured mechanical systems of n rigid bodies linked to one another by spherical, universal and/or rotational joints. The dynamic and kinematic equations are formulated on the basis of the vector-network model. The vector-network approach is a mathematical model for the systematic development of nonlinear equations describing the motion of a system of rigid bodies interconnected by kinematic joints. The entire procedure of the vector-network is an application of the basic concepts of graph theory in which laws of dynamics have been integrated.
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Kumar, Praveen, Ligesh Theeyancheri, and Rajarshi Chakrabarti. "Chemically symmetric and asymmetric self-driven rigid dumbbells in a 2D polymer gel." Soft Matter 18, no. 13 (2022): 2663–71. http://dx.doi.org/10.1039/d1sm01820e.
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Cordasco, Daniel, and Prosenjit Bagchi. "Intermittency and synchronized motion of red blood cell dynamics in shear flow." Journal of Fluid Mechanics 759 (October 24, 2014): 472–88. http://dx.doi.org/10.1017/jfm.2014.587.
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AbstractWe present the first full-scale computational evidence of intermittent and synchronized dynamics of red blood cells in shear flow. These dynamics are characterized by the coexistence of a tumbling motion in which the cell behaves like a rigid body and a tank-treading motion in which the cell behaves like a liquid drop. In the intermittent dynamics, we observe sequences of tumbling interrupted by swinging, as well as sequences of swinging interrupted by tumbling. In the synchronized dynamics, the tumbling and membrane rotation are observed to occur simultaneously with integer ratios of the rotational frequencies. These dynamics are shown to be dependent on the stress-free state of the cytoskeleton, and are explained based on the cell membrane energy landscape.
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WOLF, DIETRICH E., SILVIO R. DAHMEN, and HAYE HINRICHSEN. "SOLID FRICTION: SPINNING AT THE ONSET OF SLIDING." International Journal of Modern Physics B 21, no. 23n24 (2007): 4158–63. http://dx.doi.org/10.1142/s0217979207045347.
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The majority of experimental and theoretical friction studies considers translational motion, where all coarse-grained interface elements are displaced alike. An additional rotation of the slider introduces a well controlled displacement inhomogeneity across the interface. The friction response now consists of a force and a torque that are generally coupled. Recent results for a cylindrical slider are reviewed and applied to rigid objects with rotational symmetry about an axis. It is predicted that the difference between static and dynamic friction force can be suppressed, if a certain torque is applied. Moreover, we study the dynamics of the transition from sticking to sliding.
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Fukushima, Toshio. "A numerical scheme to integrate the rotational motion of a rigid body." Symposium - International Astronomical Union 172 (1996): 245–48. http://dx.doi.org/10.1017/s0074180900127470.
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Once, we numerically integrated the precession and nutation of a spheroidal rigid Earth (Kubo and Fukushima 1987). As a natural extension, we tried to integrate the rotation of a triaxial rigid Earth numerically and faced a problem: a loss of precision in long-term integration. This is due to the smallness of the characteristic period of the problem: 1 day. Of course, one can integrate the rotational motion in higher precision arithmetics with a smaller stepsize. However, the quadruple precision integration is roughly 30 times more time-consuming than the double precision integration. See Table 1. Therefore, it is desirable if there is a formulation 1) reducing the overall integration error, 2) being independent on the choice of the integrator and 3) requiring no extra computations. The key points to achieve this goal will be to find a set of variables which 1) are efficiently convertible to the physical quantities required finally, say, the orientation matrix in the case of the rotational dynamics, and 2) vary with time as smoothly as possible. In this note, we report a discovery of such an example.
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Dawe, J. L., A. B. Schriver, and C. Sofocleous. "Masonry infilled steel frames subjected to dynamic load." Canadian Journal of Civil Engineering 16, no. 6 (1989): 877–85. http://dx.doi.org/10.1139/l89-130.
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Experimentally determined dynamic responses of ten scale models of masonry infilled steel frames were compared with the results of three simple analytical models. Effects investigated included stiffening and strengthening contribution of the masonry infill, degradation of the system, motion intensity, frame stiffness, and rotational joint rigidity at slab-to-column intersections. Tests on one-third scale models, subjected to sinusoidal motions, revealed that masonry infill markedly increases the dynamic strength and stiffness of the system. At weak-to-moderate motions (below 0.5 g), models exhibited a nonlinear response before the final failure, while strong motions accelerated the system degradation rate. Stiffer frames and rotationally rigid joints resulted in significantly increased system dynamic strength. A braced frame model wherein cross-bracing replaces the panel action adequately predicted linear and lower-region nonlinear responses of infilled frames with flexible column-to-slab rotational conditions. Satisfactory predictions of the linear response of framed walls with rigid column-to-slab rotational conditions were made with a single degree of freedom model. The third analytical model based on an equivalent strut technique was found to be unsatisfactory for predicting dynamic response of masonry infilled frames. Key words: masonry panel, steel frame, shear, dynamic, analytical, experimental.
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Huang, Yangyang, Leif Ristroph, Mitul Luhar, and Eva Kanso. "Bistability in the rotational motion of rigid and flexible flyers." Journal of Fluid Mechanics 849 (June 26, 2018): 1043–67. http://dx.doi.org/10.1017/jfm.2018.446.
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We explore the rotational stability of hovering flight in an idealized two-dimensional model. Our model is motivated by an experimental pyramid-shaped object (Weathers et al., J. Fluid Mech, vol. 650, 2010, pp. 415–425; Liu et al., Phys. Rev. Lett., vol. 108, 2012, 068103) and a computational $\wedge$-shaped analogue (Huang et al., Phys. Fluids, vol. 27 (6), 2015, 061706; Huang et al., J. Fluid Mech., vol. 804, 2016, pp. 531–549) hovering passively in oscillating airflows; both systems have been shown to maintain rotational balance during free flight. Here, we attach the $\wedge$-shaped flyer at its apex in oscillating flow, allowing it to rotate freely akin to a pendulum. We use computational vortex sheet methods and we develop a quasi-steady point-force model to analyse the rotational dynamics of the flyer. We find that the flyer exhibits stable concave-down ($\wedge$) and concave-up ($\vee$) behaviour. Importantly, the down and up configurations are bistable and co-exist for a range of background flow properties. We explain the aerodynamic origin of this bistability and compare it to the inertia-induced stability of an inverted pendulum oscillating at its base. We then allow the flyer to flap passively by introducing a rotational spring at its apex. For stiff springs, flexibility diminishes upward stability but as stiffness decreases, a new transition to upward stability is induced by flapping. We conclude by commenting on the implications of these findings for biological and man-made aircraft.
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Fiori, Simone. "A Closed-Form Expression of the Instantaneous Rotational Lurch Index to Evaluate Its Numerical Approximation." Symmetry 11, no. 10 (2019): 1208. http://dx.doi.org/10.3390/sym11101208.
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The lurch index has recently been introduced in applied kinematics as an integral descriptor of the fluency of the motion of a rigid body in space. It may be defined in different versions, according to the component of motion under investigation. In the present paper, we analyze a rotational lurch index, which describes the fluency of the spin component of motion and whose value depends, through involved relations, on the dynamics of three canonical descriptors of the orientation of a rigid body in space. The aim of the present paper is to offer a closed-form expression of the instantaneous component of the rotational lurch, which leads to the namesake index upon integration and normalization. The closed form of the index is, then, used to evaluate its practical calculation, based on numerical approximations on a number of data sets.
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IVANCEVIC, VLADIMIR G., and TIJANA T. IVANCEVIC. "HUMAN VERSUS HUMANOID ROBOT BIODYNAMICS." International Journal of Humanoid Robotics 05, no. 04 (2008): 699–713. http://dx.doi.org/10.1142/s0219843608001595.
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In this paper we compare and contrast modern dynamical methodologies common to both humanoid robotics and human biomechanics. While the humanoid robot's motion is defined on the system of constrained rotational Lie groups SO(3) acting in all major robot joints, human motion is defined on the corresponding system of constrained Euclidean groups SE(3) of the full (rotational + translational) rigid motions acting in all synovial human joints. In both cases the smooth configuration manifolds, Q rob and Q hum , respectively, can be constructed. The autonomous Lagrangian dynamics are developed on the corresponding tangent bundles, TQ rob and TQ hum , respectively, which are themselves smooth Riemannian manifolds. Similarly, the autonomous Hamiltonian dynamics are developed on the corresponding cotangent bundles, T*Q rob and T*Q hum , respectively, which are themselves smooth symplectic manifolds. In this way a full rotational + translational biodynamics simulator has been created with 270 DOFs in total, called the Human Biodynamics Engine, which is currently in its validation stage. Finally, in both the human and the humanoid case, the time-dependent biodynamics generalizing the autonomous Lagrangian (of Hamiltonian) dynamics is naturally formulated in terms of jet manifolds.
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Attia, Hazem Ali. "Point-joint coordinate formulation for the dynamic analysis of generalised planar linkages." ANZIAM Journal 46, no. 4 (2005): 575–89. http://dx.doi.org/10.1017/s1446181100009688.
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AbstractThis paper presents a two-step formulation for the dynamic analysis of generalised planar linkages. First, a rigid body is replaced by a dynamically equivalent constrained system of particles and Newton's second law is used to study the motion of the particles without introducing any rotational coordinates. The translational motion of the constrained particles represents the general motion of the rigid body both translationally and rotationally. The simplicity and the absence of any rotational coordinates from the final form of the equations of motion are considered the main advantages of this formulation. A velocity transformation is then used to transform the equations of motion to a reduced set in terms of selected relative joint variables. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and some cut-joint constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.
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Sanz-Andre´s, Angel, Gonzalo Tevar, and Francisco-Javier Rivas. "The Forced Oscillations of Submerged Bodies." Journal of Fluids Engineering 125, no. 4 (2003): 710–15. http://dx.doi.org/10.1115/1.1593706.
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The increasing use of very light structures in aerospace applications are given rise to the need of taking into account the effects of the surrounding media in the motion of a structure (as for instance, in modal testing of solar panels or antennae) as it is usually performed in the motion of bodies submerged in water in marine applications. New methods are in development aiming at to determine rigid-body properties (the center of mass position and inertia properties) from the results of oscillations tests (at low frequencies during modal testing, by exciting the rigid-body modes only) by using the equations of the rigid-body dynamics. As it is shown in this paper, the effect of the surrounding media significantly modifies the oscillation dynamics in the case of light structures and therefore this effect should be taken into account in the development of the above-mentioned methods. The aim of the paper is to show that, if a central point exists for the aerodynamic forces acting on the body, the motion equations for the small amplitude rotational and translational oscillations can be expressed in a form which is a generalization of the motion equations for a body in vacuum, thus allowing to obtain a physical idea of the motion and aerodynamic effects and also significantly simplifying the calculation of the solutions and the interpretation of the results. In the formulation developed here the translational oscillations and the rotational motion around the center of mass are decoupled, as is the case for the rigid-body motion in vacuum, whereas in the classical added mass formulation the six motion equations are coupled. Also in this paper the nonsteady motion of small amplitude of a rigid body submerged in an ideal, incompressible fluid is considered in order to define the conditions for the existence of the central point in the case of a three-dimensional body. The results here presented are also of interest in marine applications.
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Alapati, Suresh, Wooseong Che, Sunkara Srinivasa Rao, and Giang T. T. Phan. "Simulation of an Elastic Rod Whirling Instabilities by Using the Lattice Boltzmann Method Combined with an Immersed Boundary Method." Axioms 12, no. 11 (2023): 1011. http://dx.doi.org/10.3390/axioms12111011.
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Mathematical modeling and analysis of biologically inspired systems has been a fascinating research topic in recent years. In this work, we present the results obtained from the simulation of an elastic rod (that mimics a flagellum axoneme) rotational motion in a viscous fluid by using the lattice Boltzmann method (LBM) combined with an immersed boundary method (IBM). A finite element model consists of a set of beam and truss elements used to discretize the flagellum axoneme while the fluid flow is solved by the well-known LBM. The hydrodynamic coupling to maintain the no-slip boundary condition between the fluid and the elastic rod is conducted with the IBM. The rod is actuated with a torque applied at its base cross-section that acts as a driving motor of the axoneme. We simulated the rotational dynamics of the rod for three different rotational frequencies (low, medium, and high) of the motor. To compare with previous publication results, we chose the sperm number Sp=L(4πμω)/(EI)1/4 as the validation parameter. We found that at the low rotational frequency, f = 1.5 Hz, the rod performs stable twirling motion after attaining an equilibrium state (the rod undergoes rigid rotation about its axis). At the medium frequency, f = 2.65 Hz, the rod undergoes whirling motion, where the tip of the rod rotates about the central rotational axis of the driving motor. When the frequency increases further, i.e., when it reaches the critical value, fc ≈ 2.7 Hz, the whirling motion becomes over-whirling, where the tip of the filament falls back to the base and performs a steady crank-shafting motion. All three rotational dynamics, twirling, whirling, and over-whirling, and the critical value of rotational frequency are in good agreement with the previously published results. We also observed that our present simulation technique is computationally more efficient than previous works.
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Artale, Valeria, Cristina L. R. Milazzo, and Angela Ricciardello. "A quaternion-based simulation of multirotor dynamics." International Journal of Modeling, Simulation, and Scientific Computing 06, no. 01 (2015): 1550009. http://dx.doi.org/10.1142/s1793962315500099.
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The main problem addressed in this paper is the quaternion-based trajectory control of a microcopter consisting of six rotors with three pairs of counter-rotating fixed-pitch blades, known as hexacopter. If the hypothesis of rigid body condition is assumed, the Newton–Euler equations describe the translational and rotational motion of the drone. The standard Euler-angle parametrization of three-dimensional rotations contains singular points in the coordinate space that can cause failure of both dynamical model and control. In order to avoid singularities, all the rotations of the microcopter are thus parametrized in terms of quaternions and an original proportional derivative (PD) regulator is proposed in order to control the dynamical model. Numerical simulations will be performed on symmetrical flight configuration, proving the reliability of the proposed PD control technique.
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Leshchenko, Dmytro, and Tetiana Kozachenko. "Evolution of rotations of a spheroid with cavity containing a viscous fluid in a resistive medium." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 35 (January 28, 2022): 152–60. http://dx.doi.org/10.37069/1683-4720-2021-35-11.
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The problems of the dynamics of rigid bodies with the fluid containing cavities are classical problems of mechanics. The interest to the problems of rotations of rigid bodies with the fluid-containing cavities increased with the development of the rocket and space technology. There is a necessity to study the problems of the dynamics of bodies with cavities containing a viscous fluid, to calculate the motion of spacecraft about the its center of mass, as well as their orientation and stabilization. The torques of forces of viscous fluid in cavity, acting on the body, are often relatively small and can be considered as perturbations. It is natural to use the methods of small parameter to analyze the dynamics of rigid body under the action of applied torques. The method applied in this paper is the Krylov--Bogoliubov asymptotic averaging method. The paper develops on approximate solution by means of averaging method to the system of Euler's equations with additional perturbation terms for a spheroid filled with a viscous fluid in a resistive medium. The numerical integration of the averaged system of equations is conducted for the body motion. The graphical presentations of the solutions are represented and discussed. The main objective of this paper is to extend the previous results for the problem of motion about a center of mass of a spheroid with a cavity filled with a fluid of high viscosity (in the absence of resistive medium). Evolution of perturbed Euler--Poinsot motion under the influence of small internal and external torques is studied. We present new qualitative and quantitative results of investigations of motion in a resistive medium of a nearly dynamically spherical rigid body with a cavity containing viscous fluid with small Reynolds number. We received the system of motion equations in standard form, which refined in square approximation by small parameter. The averaging method was applied to the nonlinear system equation of rotational motion. In this paper we present the input equations of motion, conduct an averaging procedure and receive the averaged equations which, being simpler than the original ones, describe the motion over the large time interval. We establish qualitative and quantitative properties of motion and provide a description of the evolution of the body motion. Results summed up in this paper make it possible to analyze motions of artificial satellites and celestial bodies under the action of small perturbation torques.
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Nakanishi, Y., Y. Funami, and T. Yano. "Motion analysis of a power unit moored with a cable for tidal power generation (2D calculation considering fluid forces acting on the unit and cable)." Journal of Physics: Conference Series 2217, no. 1 (2022): 012037. http://dx.doi.org/10.1088/1742-6596/2217/1/012037.
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Abstract The power unit with counter-rotating propellors has been proposed for a tidal power generation. The unit has the potential to be moored with a cable because of inherent equilibrium of the rotational moments acting on the counter-rotating propellors. On the other hand, the flow condition of a tidal current is not steady, therefore, the motion and the posture of the power unit should be investigated for the stability of the power generation in terms of the fluid dynamics. In this study, the two-dimensional motion of the power unit and the cable modelled with rigid elements connected each other with pivots are analyzed as the combination of translational and rotational motions with the constraint of the connected elements. The time-dependent position, angle and relative velocity of each calculation element were obtained to validate the usefulness of the proposed method.
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de Souza, Alain G., and Luiz C. G. de Souza. "Satellite Attitude Control System Design Taking into Account the Fuel Slosh and Flexible Dynamics." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/820586.
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The design of the spacecraft Attitude Control System (ACS) becomes more complex when the spacecraft has different type of components like, flexible solar panels, antennas, mechanical manipulators and tanks with fuel. The interaction between the fuel slosh motion, the panel’s flexible motion and the satellite rigid motion during translational and/or rotational manoeuvre can change the spacecraft center of mass position damaging the ACS pointing accuracy. This type of problem can be considered as a Fluid-Structure Interaction (FSI) where some movable or deformable structure interacts with an internal fluid. This paper develops a mathematical model for a rigid-flexible satellite with tank with fuel. The slosh dynamics is modelled using a common pendulum model and it is considered to be unactuated. The control inputs are defined by a transverse body fixed force and a moment about the centre of mass. A comparative investigation designing the satellite ACS by the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) methods is done. One has obtained a significant improvement in the satellite ACS performance and robustness of what has been done previously, since it controls the rigid-flexible satellite and the fuel slosh motion, simultaneously.
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Schastok, J., M. Soffel, H. Ruder, and M. Schneider. "The post - Newtonian rotation of Earth: a first approach." Symposium - International Astronomical Union 128 (1988): 341–47. http://dx.doi.org/10.1017/s0074180900119709.
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The problems of dynamics of extended bodies in metric theories of gravity are reviewed. In a first approach towards the relativistic description of the Earth's rotational motion the post - Newtonian treatment of the free precession of a pseudo - rigid and axially symmetric model Earth is presented. Definitions of angular momentum, pseudo - rigidity, the corotating frame, tensor of inertia and axial symmetry of the rotating body are based upon the choice of the standard post - Newtonian (PN) coordinates and the full PN energy momentum complex. In this framework, the relation between angular momentum and angular (coordinate) velocity is obtained. Since the PN Euler equations for the angular velocity here formally take their usual Newtonian form it is concluded that apart from PN modifications (renormalizations) of the inertia tensor, the rotational motion of our pseudo - rigid and axially symmetric model Earth essentially is “Newtonian”.
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Wall, A. S., R. G. Langlois, and F. F. Afagh. "Modeling Helicopter Blade Sailing: Dynamic Formulation in the Planar Case." Journal of Applied Mechanics 74, no. 6 (2007): 1104–13. http://dx.doi.org/10.1115/1.2722766.
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As part of a research project aimed at simulating rotor dynamic response during shipboard rotor startup and shutdown operations, a dynamic model of the ship–helicopter–rotor system that is appropriate for use in predicting rotor elastic response was developed. This planar model consists of a series of rigid bodies connected by rotational stiffness and damping elements that allow motion in the flapwise direction. The rotors were partitioned into an arbitrary number of rigid beam segments having the inertial and geometrical properties of a typical rotor. Helicopter suspension flexibility and damping were also modeled, although the helicopter was otherwise considered as a rigid body. Lagrange’s equation was used to derive the governing dynamic equations for the helicopter–rotor model. The effect of ship motion on blade deflection was also considered. The ship motion supplied as input to the model included representative frigate flight deck motion in three dimensions corresponding to an actual sea spectrum, ship particulars and ship operating conditions. This paper is intended to detail the dynamic approach adopted for this blade sailing study, and its conceptual validation in the planar case. The methodologies that have been developed lend themselves to easy expansion into three dimensions, and into torsion and lead/lag modeling. The amount of blade motion induced by ship motion on nonrotating helicopter blades is included. Although aerodynamic loads are a major contributor to blade sailing, this paper focuses on the dynamics aspect of the problem, and thus does not include aerodynamic effects.
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Cheng, J. K., and K. W. Wang. "Stability and Nonlinear Dynamics of a Horizontally Base-Excited Rigid Rod With Unsymmetric End Stiffnesses." Journal of Vibration and Acoustics 115, no. 1 (1993): 85–95. http://dx.doi.org/10.1115/1.2930320.
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This paper presents a dynamic analysis of a horizontally base-excited rigid rod with unsymmetric end stiffnesses. This is to model a shaker/mould structure with gripper imperfections. The study explains the large rotational and transverse vibrations of the mould at specific operating frequencies observed in the experiments. The governing equations consist of a time-dependent coefficient which indicates the existence of parametric excitation effects. It is concluded that differences between the gripper stiffnesses are responsible for this phenomenon and could destabilize the system. The value of the time-varying parameter is related to the horizontal vibration amplitude of the mould and hence is a function of the system parameters and excitation frequency. The mould’s rotational motion is directly parametrically excited while its transverse vibration is excited indirectly through coupling with the rotational motion. A thorough analysis of this class of mechanical systems has not been performed in the past. In this research, studies are conducted to identify the contributions of various system parameters, such as gripper stiffness, damping, mould inertia, and excitation amplitude to the system dynamic characteristics. The results provide new insight and guidelines toward optimizing such mechanical systems.
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McPhee, J. J., and R. N. Dubey. "Dynamics of Multibody Systems With Known Configuration Changes." Journal of Applied Mechanics 58, no. 1 (1991): 215–21. http://dx.doi.org/10.1115/1.2897153.
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The equations of motion are derived for a system with inertial properties that are varying in time as a result of known relative motions between the rigid bodies comprising the system. This vector-dyadic formulation has been encoded into a computer program, making use of the conformal rotation vector for the representation of rotations. The numerical simulation of two different physical systems is presented in order to illustrate the dynamic effects of the changing inertial properties, and the usefulness of the encoded formulation for modeling these effects.
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Weiss, A., R. G. Langlois, and M. J. D. Hayes. "Dynamics and vibration analysis of the interface between a non-rigid sphere and omnidirectional wheel actuators." Robotica 33, no. 9 (2014): 1850–68. http://dx.doi.org/10.1017/s0263574714001088.
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SUMMARYThis paper presents analysis of the dynamics and vibration of an orientation motion platform utilizing a sphere actuated by omnidirectional wheels. The purpose of the analysis is to serve as a design tool for the construction of a six-degree-of-freedom motion platform with unlimited rotational motion. The equations of motion are presented taking flexibility of the system into account. The behaviour of the system is illustrated by sample configurations with a range of omnidirectional wheel types and geometries. Vibration analysis follows, and sensitivity to various parameters is investigated. It is determined that the geometry of omnidirectional wheels has a significant effect on the behaviour of the system.
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Харыбина, I. Kharybina, Новикова, Tatyana Novikova, Новиков, and Aleksandr Novikov. "Study of the Rotational Motion of a Rigid Body in Profile School Elective Courses." Profession-Oriented School 4, no. 3 (2016): 40–45. http://dx.doi.org/10.12737/20561.
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The article deals with the problem of studying the rotational motion of a rigid body in a physics course at profi le school. It is proposed to supplement the
 study of the topic elective courses to meet the challenges of the kinematics, dynamics, conservation laws for describing plane-parallel motion of a solid
 body. The article gives examples of jobs on the formation method of fi nding instantaneous center of velocity, methods are provided for the activities of
 the students at the school level action.
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Banerjee, A. K., and T. R. Kane. "Dynamics of a Plate in Large Overall Motion." Journal of Applied Mechanics 56, no. 4 (1989): 887–92. http://dx.doi.org/10.1115/1.3176187.
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Equations of motion are formulated for a thin elastic plate that is executing small motions relative to a reference frame undergoing large rigid body motions (three-dimensional rotation and translation) in a Newtonian reference frame. As an illustrative example, a spin-up maneuver for a simply-supported rectangular plate is examined, and the vibration modes of such a plate are used to show that the present theory captures the phenomenon of dynamic stiffening.
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Sherif, Karim, Karin Nachbagauer, and Wolfgang Steiner. "On the rotational equations of motion in rigid body dynamics when using Euler parameters." Nonlinear Dynamics 81, no. 1-2 (2015): 343–52. http://dx.doi.org/10.1007/s11071-015-1995-3.
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Limpouchová, Zuzana, Karel Procházka, Vlastimil Fidler, Jiří Dvořák, and Bohumil Bednář. "Molecular Movements and Dynamics in Solutions Studied by Fluorescence Depolarization Measurement." Collection of Czechoslovak Chemical Communications 58, no. 2 (1993): 213–33. http://dx.doi.org/10.1135/cccc19930213.
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Theories allowing interpretation of the results of time-resolved polarization spectrofluorimetry in solutions are reviewed and their applicability under various conditions is discussed. For the reorientation of rigid molecules in an isotropic medium, the most frequently employed models are presented, such as rotational diffusion model, the Fokker-Planck-Langevin model, etc. Systems with internal rotation, systems in anisotropic media, systems with a complex electron relaxation and systems with energy transfer are discussed as examples of more complex systems. A special attention is devoted to the polarization fluorimetry of probes bound to/or sorbed at polymer and biopolymer chains. The review focuses on theoretical models of reorientational motion for interpretation of fluorescence anisotropy decays. Experimental studies and computer simulations are discussed only when it is necessary for comparison with theoretical predictions. Complicated models for simultaneous reorientational motion and energy transfer, solvent relaxation, etc., although very important for many applications, exceed the scope of this review and are mentioned only very briefly.
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Geschwindner, Christopher, Maren Werner, Laurent André, et al. "High-Resolution Two-Phase Velocimetry Of Aspherical Particles Using Wavelet-Based Optical Flow Velocimetry (WOFV) Benchmarked With Fully Resolved Direct Numerical Simulations." Proceedings of the International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics 21 (July 8, 2024): 1–21. http://dx.doi.org/10.55037/lxlaser.21st.101.
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Several techniques exist to measure the carrier and dispersed phases in multi-phase flows. Particle image velocimetry (PIV) analyzes the carrier phase by cross-correlating particle images, but its resolution is limited by the size of the interrogation window, making it difficult to resolve fine-scale turbulent structures. Particle tracking algorithms capture translational motion of dispersed particles well, but struggle with rotational motion, especially for irregular and aspherical particles. Currently, there is no method that universally measures both the carrier phase velocity field and the translational and rotational motions of dispersed particles. This study evaluates wavelet-based optical flow velocimetry (wOFV) for motion estimation in multi-phase flows, focusing on dispersed ellipsoidal particles and their surrounding turbulent carrier flow using synthetic image data. The research proceeds in two phases: first, the rigid motion of ellipses, including translational and rotational components, is analyzed using wOFV-generated dense motion fields. The results highlight the critical role of the regularization weighting parameter λ. Higher λ values improve translational motion estimation, while an optimal λ avoids under-regularization and non-physical structures in rotational motion. wOFV maintains accuracy in combined motion scenarios with optimal λ values. In the second phase, wOFV captures the turbulent carrier flow around an aspherical particle, benchmarked against DNS data and compared to PIV. wOFV outperforms PIV in resolving finer structures near the particle surface and in accurately representing the wake region. Error analyses confirm wOFV’s superior performance, with optimal results within a specific λ range. In conclusion, wOFV is a highly effective tool for the analysis of multi-phase flow dynamics, providing greater resolution and accuracy than PIV, especially in complex scenarios involving aspherical particles.
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Gao, YY, SH Li, JL Xu, DY Wang, and RH Wang. "Research progress in molecular dynamics of high-performance PBO fibers." Journal of Physics: Conference Series 2460, no. 1 (2023): 012139. http://dx.doi.org/10.1088/1742-6596/2460/1/012139.
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Abstract This article reviews the application and development of molecular dynamics in the field of poly(p-benzobisoxazole) (PBO) molecules, including the use of molecular dynamics simulations to calculate the theoretical Young’s modulus of PBO molecules and discuss them from the perspective of molecular theory Combine the rotational isomerism state theory with the long molecular dynamics simulation of small fragments to evaluate the limit length of the persistence vector a. The molecular dynamics calculation is used to study the molecular motion behavior of isolated rigid rod molecules such as PBO. Combining computer simulation technology and X-ray diffraction data collected by the imaging board system to analyze the crystal structure of the PBO fiber, and use molecular dynamics and dynamic modeling to establish the PBO/epoxy interface and study its performance.
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Arkhipova, Inga. "Dynamics of a rigid rotor in the elastic bearings." Theoretical and Applied Mechanics 31, no. 1 (2004): 73–83. http://dx.doi.org/10.2298/tam0401073a.
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As a rule in the studies of a rigid rotor in the elastic bearings the authors consider the linear system corresponding to the plane-parallel motion and the effect of self-centring under unlimited growth of the rotation frequency. In the present paper rotor is considered as a mechanical system with four degrees of freedom. Different motions of a statically and dynamically unbalanced vertical rotor supported in the non-linear bearings are studied.
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Grace, I. F., and R. A. Ibrahim. "Modelling and analysis of ship roll oscillations interacting with stationary icebergs." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 10 (2008): 1873–84. http://dx.doi.org/10.1243/09544062jmes935.
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Impact dynamic interaction of ships with solid ice or stationary rigid structures is a serious problem that affects the safe operation and navigation in arctic regions. The purpose of this study is to present two analytical models of impact interaction between ship roll dynamics and one-side rigid barrier. These models are the phenomenological modelling represented by a power law in stiffness and damping forces, and Zhuravlev non-smooth coordinate transformation. Extensive numerical simulations are carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequencies of external wave roll moment. The basins of attraction of safe operation are obtained and reveal the coexistence of different response regimes such as non-impact periodic oscillations, modulation impact motion, period-added impact oscillations, chaotic impact motion, and unbounded rotational motion. The results are summarized in the bifurcation diagram in terms of response-excitation amplitudes plane. The stability fraction index is obtained for different values of excitation frequency based on the ratio of the area of bounded roll oscillations to the total area of the grazing orbit.
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McCann, Brennan, and Morad Nazari. "Control and maintenance of fully-constrained and underconstrained rigid body motion on Lie groups and their tangent bundles." Journal of Geometric Mechanics 14, no. 1 (2022): 29. http://dx.doi.org/10.3934/jgm.2022002.
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<p style='text-indent:20px;'>Presented herein are a class of methodologies for conducting constrained motion analysis of rigid bodies within the Udwadia-Kalaba (U-K) formulation. The U-K formulation, primarily devised for systems of particles, is advanced to rigid body dynamics in the geometric mechanics framework and a novel development of U-K formulation for use on nonlinear manifolds, namely the special Euclidean group <inline-formula><tex-math id="M1">\begin{document}$ {\mathsf{SE}(3)}$\end{document}</tex-math></inline-formula> and its second order tangent bundle <inline-formula><tex-math id="M2">\begin{document}${\mathsf{T}^2\mathsf{SE}(3)} $\end{document}</tex-math></inline-formula>, is proposed in addition to the formulation development on Euclidean spaces. Then, a Morse-Lyapunov based tracking controller using backstepping is applied to capture disturbed initial conditions that the U-K formulation cannot account for. This theoretical development is then applied to fully-constrained and underconstrained scenarios of rigid-body spacecraft motion in a lunar orbit, and the translational and rotational motions of the spacecraft and the control inputs obtained using the proposed methodologies to achieve and maintain those constrained motions are studied.</p>
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Ma, Chao, Yu Qing Liu, and Xiu Qing Zhu. "Research of Human Modeling and Motion Simulation Based on ADAMS." Advanced Materials Research 1016 (August 2014): 292–97. http://dx.doi.org/10.4028/www.scientific.net/amr.1016.292.
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The human model in this paper is simplified as a rigid body of 15 segments and the Roberson-Wittenberg method is used to establish the equation of conservation of angular momentum to obtain the control methods of human self-rotation without external force in a weightless environment. And simulation of human dynamic is completed in ADMAS (Automatic Dynamic Analysis of mechanical Systems). The simulation results show that human can generate corresponding body rotation through own limbs rotation in the weightless, and body rotation velocity and angle increase with the moment of inertia and rotational velocity of active body that adds greater torque to joint. Through the analysis of the impact of the angular velocity and torque on the body rotation, a set of self-rotation control strategy for astronaut is proposed in weightless environment.
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Arimoto, Suguru, Pham Thuc Anh Nguyen, Hyun-Yong Han, and Zoe Doulgeri. "Dynamics and control of a set of dual fingers with soft tips." Robotica 18, no. 1 (2000): 71–80. http://dx.doi.org/10.1017/s0263574799002441.
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This paper attempts firstly to derive a mathematical model of the dynamics of a set of dual fingers with soft and deformable tips which grasps and manipulates a rigid object with some dexterity. To gain a physical insight into the problem, consideration is restricted to the case that the motion of the whole system is confined to a horizontal plane. Secondly on the basis of the derived model it is shown that the rotation of the object can be indirectly controlled by the change of positions of the center points of both contact areas on the object. Then, each of the center points of contact areas can be positioned by inclining the last link of each corresponding finger against the object. It is further shown that, when both forces of pressing the object becomes almost equal, the equation of motion of the object in terms of rotational angles assumes the form of a harmonic oscillator with a forcing term, which can be regulated coordinately by the relative angle between the two last links contacting with the object. It is also shown that dynamics of this system satisfy passivity. Finally, design problems of control for dynamic stable grasping and enhancing dexterity in manipulating things are discussed on the basis of passivity analysis.
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Amare, Zemichael, Bin Zi, Sen Qian, and Lei Zu. "Dynamic analysis of electrohydraulic cable-driven parallel robots." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 10 (2018): 3400–3416. http://dx.doi.org/10.1177/0954406218815715.
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Dynamic analysis is required for achieving higher efficiency of cable-driven parallel robots. This paper presents the dynamic analysis of the cable-driven parallel robots using the Lagrange’s method, taking cable’s mass and elasticity into account. The Lagrange’s equations of motion are derived and evaluated for the generalized coordinates of the system. The dynamic motion of the parallel robot is expressed by the generalized forces and generalized coordinates to completely specify the configuration of the whole mechanical system as well as every component of the system. The cables are modeled to control and design the motion of each part of the rigid body. The elasticity is determined using the optimal cable’s tensions and lengths. Numerical simulations are performed to obtain the dynamic motion of the cable-driven parallel robots and. Experimental analyses and the effect of the mass of the end-effector on the cable’s tension and elasticity are also investigated. These examples illustrate that the general motion of the rigid body is superior described in terms of a set of independent coordinates. The results indicate that a better speed of the end-effector can be achieved by adding the linear and rotational motions of the electrohydraulic cylinder actuators into the traditional cable-driven parallel robots.
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Mason, Justice J., Christine Allen-Blanchette, Nicholas Zolman, Elizabeth Davison, and Naomi Ehrich Leonard. "Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distribution." Aerospace 10, no. 11 (2023): 921. http://dx.doi.org/10.3390/aerospace10110921.
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In many real-world settings, image observations of freely rotating 3D rigid bodies may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation techniques to learn the dynamics. The usefulness of standard deep learning methods is also limited, because an image of a rigid body reveals nothing about the distribution of mass inside the body, which, together with initial angular velocity, is what determines how the body will rotate. We present a physics-based neural network model to estimate and predict 3D rotational dynamics from image sequences. We achieve this using a multi-stage prediction pipeline that maps individual images to a latent representation homeomorphic to SO(3), computes angular velocities from latent pairs, and predicts future latent states using the Hamiltonian equations of motion. We demonstrate the efficacy of our approach on new rotating rigid-body datasets of sequences of synthetic images of rotating objects, including cubes, prisms and satellites, with unknown uniform and non-uniform mass distributions. Our model outperforms competing baselines on our datasets, producing better qualitative predictions and reducing the error observed for the state-of-the-art Hamiltonian Generative Network by a factor of 2.
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Kondora, Grzegorz, and Dariusz Asendrych. "Modelling the Dynamics of Flexible and Rigid Fibres." Chemical and Process Engineering 34, no. 1 (2013): 87–100. http://dx.doi.org/10.2478/cpe-2013-0008.
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Abstract A particle-level simulation technique has been developed for modelling fibre suspension flow in a converging channel of a papermachine headbox. The fibre model is represented by a chain of elements connected together. The model was verified by the simulation of rigid fibre dynamics in a simple shear flow. The period of rotation was found to be in a very good agreement with theory and reference data. The model was then employed to simulate fibre motion in a converging channel of a papermachine headbox. Fibre suspension motion was resolved using two-step procedure. Velocity field was calculated by means of a commercial CFD code ANSYS Fluent with RSM turbulence model applied and used as an input to the in-house code allowing to simulate fibre dynamics. Results of the calculations were used to construct the fibre orientation probability distribution (FOPD) which was found to be consistent with available experimental data.
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Hwang, Yunn Lin, and Shen Jenn Hwang. "Solving for Dynamic Problems in Flexible Manufacturing Systems." Advanced Materials Research 156-157 (October 2010): 1501–4. http://dx.doi.org/10.4028/www.scientific.net/amr.156-157.1501.
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Generally speaking, the flexible manufacturing systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, a recursive formulation is developed for the dynamic analysis of open-loop flexible manufacturing systems. The nonlinear generalized Newton-Euler equations are developed for rigid and deformable bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve equations of motion for open-loop systems consisting of interconnected rigid and deformable bodies is presented in this paper. This method applies recursive method with the Newton-Euler method for deformable bodies to obtain a large, loosely coupled system equations of motion. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the modern computer systems. The algorithms presented in this paper are demonstrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The recursive formulation developed in this investigation is illustrated by a practical numerical example.
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Leshchenko, D., and T. Kozachenko. "PERTURBED MOTIONS OF A RIGID BODY WITH A MOVABLE MASS IN A RESISTIVE MEDIUM." Mechanics And Mathematical Methods 5, no. 2 (2023): 16–24. http://dx.doi.org/10.31650/2618-0650-2023-5-2-16-24.
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Various cases of the rigid body motion having internal degrees of freedom was studied. In particular, the motions of a body carrying masses which are attached to it by means of elastic forces with linear damping was investigated. This situation simulates the presence of loosely fixed components on a spacecraft, having a significant influence on its motion about its center of mass. The development of research in dynamics of rigid body motions about its center of mass goes in the direction of taking into account the fact that these bodies are not perfectly rigid but are rather close to perfect models. The need for the analysis of the influence of various deviations from perfectness is caused by growing accuracy requirements in space exploration, gyroscopy, etc. The influence of imperfections can be revealed using asymptotic methods of nonlinear mechanics (averaging, singular perturbations and others). This influence reduces the additional terms in the Euler equations of motion of a fictitious rigid body. In the space flight, there arises sometimes a necessity to suppress the chaotic rotation that occurs for one reason to another. Тo this end, the relative displacements of movable masses are used. A number of works are devoted to the analysis of various problems of the dynamics of space vehicles containing internal masses. The issues of stability and instability and the problems of control and stabilization of motions have been studied. In [1, 6] vector equation which describes the change of vector in the system of coordinates connected with the body was obtained. Function in the right-hind side of this equation is a polynomial containing the fourth and fifth powers of . We study the problem of the motion in a resistive medium of a dynamically symmetric rigid body carrying a movable point mass, connected with the body by an elastic coupling in the presence of viscous friction. By means of asymptotic approach equations of motion of body with mass are simplified. Nonlinear evolution of angular motions of the body is analyzed using averaged equations and numerical integration. Results summed up in this paper make it possible to analyze angular motions of artificial satellites under the influence of small internal perturbation torques.
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Cartmell, M. P., L. Morrish, and A. J. Taylor. "Dynamics of spreader motion in a gantry crane." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 212, no. 2 (1998): 85–105. http://dx.doi.org/10.1243/0954406981521060.
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This paper illustrates the steps necessary to model the dynamics of a model rubber-tyred gantry (RTG) crane as used in container-handling operations. Various modelling criteria are discussed with the emphasis placed on the importance of non-linear coupling between the chosen system coordinates. The machine is treated as three rigid bodies, these being the gantry itself, the trolley (which is constrained to lateral motion across the top beam) and the spreader. Tyre deformations and structural deflections are not considered in this work. The paper culminates in three non-linear ordinary differential equations, which are then solved numerically for a variety of different cases. An important feature of this work is that the dynamic simulations include complicated gantry motions, not currently designed for, such as combined translations and simultaneous rotations. Such motions are more commonly encountered in mobile robots. However, RTG design needs to move in this general direction in the future if significant and potential performance gains are actually to be realized in practise. The paper concludes with suggestions for implementation of the dynamic model within a fuzzy logic control system.
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Liu, Yue, Xin Li, Ying-Jing Qian, and Hong-Lei Yang. "Rigid-Flexible Coupled Dynamic and Control for Thermally Induced Vibration and Attitude Motion of a Spacecraft with Hoop-Truss Antenna." Applied Sciences 12, no. 3 (2022): 1071. http://dx.doi.org/10.3390/app12031071.
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As space exploration activities are developing rapidly, spacecraft with large antennas have gained wide acceptance in providing reliable telecommunications and astrophysical observations. In this paper, the dynamic responses and control strategy for a spacecraft with a large hoop-truss antenna under solar flux shock are studied. According to the momentum and angular momentum principle, the rigid-flexible coupled rotational dynamic equation and the translational dynamic equation of the system are established, which include the attitude motion of the rigid main body and the vibration of the antenna. Then, a finite element model of the antenna is established to analytically obtain the corresponding vibration modal shape matrix and natural frequencies. Last, the coupled responses for the attitude motion and vibration are investigated. The corresponding control strategy is designed based on a double-loop structure sliding mode control method. The Lyapunov method is used to demonstrate the global asymptotic stability of the system. Simulations verify the effectiveness of the proposed rigid-flexible coupled model and control strategy.
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Pashkevich, V. V. "Rers2014 and Mrs2014: New High-Precision Rigid Earth Rotation and Moon Rotation Series." Artificial Satellites 50, no. 1 (2015): 35–40. http://dx.doi.org/10.1515/arsa-2015-0003.
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Abstract Numerical investigation of the Earth and Moon rotational motion dynamics is carried out at a long time intervals. In our previous studies (Pashkevich, 2013), (Pashkevich and Eroshkin, 2011) the high-precision Rigid Earth Rotation Series (designated RERS2013) and Moon Rotation Series (designated MRS2011) were constructed. RERS2013 are dynamically adequate to the JPL DE422/LE422 (Folkner, 2011) ephemeris over 2000 and 6000 years and include about 4113 periodical terms (without attempt to estimate new subdiurnal and diurnal periodical terms). MRS2011 are dynamically adequate to the JPL DE406/LE406 (Standish, 1998) ephemeris over 418, 2000 and 6000 years and include about 1520 periodical terms. In present research have been improved the Rigid Earth Rotation Series RERS2013 and Moon Rotation Series MRS2011, and as a result have been constructed the new high-precision Rigid Earth Rotation Series RERS2014 and Moon Rotation Series MRS2014 dynamically adequate to the JPL DE422/LE422 ephemeris over 2000 and 6000 years, respectively. The elaboration of RERS2013 is carried out by means recalculation of sub-diurnal and diurnal periodical terms. The residuals in Euler angles between the numerical solution and RERS2014 do not surpass 3 ìas over 2000 years. Improve the accuracy of the series MRS2011 is obtained by using the JPL DE422/LE422 ephemeris. The residuals in the perturbing terms of the physical librations between the numerical solution and MRS2014 do not surpass 8 arc seconds over 6000 years