Journal articles: 'Newton-Euler equations'

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Bock, Hans Georg, Jürgen Gutekunst, Andreas Potschka, and María Elena Suaréz Garcés. "A Flow Perspective on Nonlinear Least-Squares Problems." Vietnam Journal of Mathematics 48, no. 4 (October 3, 2020): 987–1003. http://dx.doi.org/10.1007/s10013-020-00441-z.

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AbstractJust as the damped Newton method for the numerical solution of nonlinear algebraic problems can be interpreted as a forward Euler timestepping on the Newton flow equations, the damped Gauß–Newton method for nonlinear least squares problems is equivalent to forward Euler timestepping on the corresponding Gauß–Newton flow equations. We highlight the advantages of the Gauß–Newton flow and the Gauß–Newton method from a statistical and a numerical perspective in comparison with the Newton method, steepest descent, and the Levenberg–Marquardt method, which are respectively equivalent to Newton flow forward Euler, gradient flow forward Euler, and gradient flow backward Euler. We finally show an unconditional descent property for a generalized Gauß–Newton flow, which is linked to Krylov–Gauß–Newton methods for large-scale nonlinear least squares problems. We provide numerical results for large-scale problems: An academic generalized Rosenbrock function and a real-world bundle adjustment problem from 3D reconstruction based on 2D images.

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Shabana, A. A. "Dynamics of Flexible Bodies Using Generalized Newton-Euler Equations." Journal of Dynamic Systems, Measurement, and Control 112, no. 3 (September 1, 1990): 496–503. http://dx.doi.org/10.1115/1.2896170.

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A force acting on a rigid body produces a linear acceleration for the whole body together with an angular acceleration about its center of mass. This result is in fact Newton-Euler equations which are used as basis for developing many recursive formulations for open loop multibody systems consisting of interconnected rigid bodies. In this paper, generalized Newton-Euler equations are developed for deformable bodies that undergo large translational and rotational displacements. The configuration of the deformable body is identified using coupled sets of reference and elastic variables. The nonlinear generalized Newton-Euler equations are formulated in terms of a set of time invariant scalars and matrices that depend on the spatial coordinates as well as the assumed displacement field. A set of intermediate reference frames having no mass or inertia are introduced for the convenience of defining various joints between interconnected deformable bodies. The use of the obtained generalized Newton-Euler equations for developing recursive dynamic formulation for open loop deformable multibody systems containing revolute, prismatic and cylindrical joints is also discussed. The development presented in this paper demonstrates the complexities of the formulation and the difficulties encountered when the equations of motion are defined in the joint coordinate systems.

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Bascetta, Luca, Gianni Ferretti, and Bruno Scaglioni. "Closed form Newton–Euler dynamic model of flexible manipulators." Robotica 35, no. 5 (November 17, 2015): 1006–30. http://dx.doi.org/10.1017/s0263574715000934.

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SUMMARYIn this paper, a closed-form dynamic model of flexible manipulators is developed, based on the Newton–Euler formulation of motion equations of flexible links and on the adoption of the spatial vector notation. The proposed model accounts for two main innovations with respect to the state of the art: it is obtained in closed form with respect to the joints and modal coordinates (including the quadratic velocity terms) and motion equations of the whole manipulator can be computed for any arbitrary shape of the links and any possible link cardinality starting from the output of several commercial (finite element analysis) FEA codes. The Newton–Euler formulation of motion equations in terms of the joint and elastic variables greatly improves the simulation performances and makes the model suitable for real-time control and active vibration damping. The model has been compared with literature benchmarks obtained by the classical multibody approach and further validated by comparison with experiments collected on an experimental manipulator.

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Xu, Xiang-Rong, Won-Jee Chung, Young-Hyu Choi, and Xiang-Feng Ma. "A new dynamic formulation for robot manipulators containing closed kinematic chains." Robotica 17, no. 3 (May 1999): 261–67. http://dx.doi.org/10.1017/s0263574799001320.

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This paper presents a new recursive algorithm of robot dynamics based on the Kane's dynamic equations and Newton-Euler formulations. Differing from Kane's work, the algorithm is general-purpose and can be easily realized on computers. It is suited not only for robots with all rotary joints but also for robots with some prismatic joints. Formulations of the algorithm keep the recurrence characteristics of the Newton-Euler formulations, but possess stronger physical significance. Unlike the conventional algorithms, such as the Lagrange and Newton-Euler algorithm, etc., the algorithm can be used to deal with dynamics of robots containing closed chains without cutting the closed chains open. In addition, this paper makes a comparison between the algorithm and those conventional algorithms from the number of multiplications and additions.

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Hwang, Yunn-Lin, and Van-Thuan Truong. "Dynamic Analysis and Control of Multi-Body Manufacturing Systems Based on Newton–Euler Formulation." International Journal of Computational Methods 12, no. 02 (March 2015): 1550007. http://dx.doi.org/10.1142/s0219876215500073.

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This paper presents the numerical dynamic analysis and control of multi-body manufacturing systems based on Newton–Euler formulation. The models of systems built with dynamical parameters are executed. The research uses Newton–Euler formulation application in mechanics calculations, where relations between contiguous bodies through joints as well as their constrained equations are considered. The kinematics and dynamics are both analyzed and acquired by practical applications. Numerical tools help to determine all dynamic characteristics of multi-body manufacturing systems such as displacements, velocities, accelerations and reaction forces of bodies and joints. Using the acquisition, the dynamic approach of multi-body manufacturing systems is developed then whole fundamentals for controller tuning are obtained. It leads to an effective solution for mechanical manufacturing system investigation. Numerical examples are also presented as the illustrations in this paper. The numerical results imply that numerical equations based on Newton–Euler algorithm are valuable in multi-body manufacturing system. It is an effective approach for solving whole mechatronic manufacturing systems including structures, kinematics, dynamics and control.

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Whittlesey, Saunders N., and Joseph Hamill. "An Alternative Model of the Lower Extremity during Locomotion." Journal of Applied Biomechanics 12, no. 2 (May 1996): 269–79. http://dx.doi.org/10.1123/jab.12.2.269.

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An alternative to the Iterative Newton-Euler or linked segment model was developed to compute lower extremity joint moments using the mechanics of the double pendulum. The double pendulum model equations were applied to both the swing and stance phases of locomotion. Both the Iterative Newton-Euler and double pendulum models computed virtually identical joint moment data over the entire stride cycle. The double pendulum equations, however, also included terms for other mechanical factors acting on limb segments, namely hip acceleration and segment angular velocities and accelerations Thus, the exact manners in which the lower extremity segments interacted with each other could be quantified throughout the gait cycle. The linear acceleration of the hip and the angular acceleration of the thigh played comparable roles to muscular actions during both swing and stance.

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Gupta, S., and M. A. Townsend. "On the Equations of Motion for Robot Arms and Open Kinematic Chains." Journal of Mechanisms, Transmissions, and Automation in Design 110, no. 3 (September 1, 1988): 287–94. http://dx.doi.org/10.1115/1.3267460.

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The closed-form equations of motion for robot arms and other open kinematic chains are derived using the Newton-Euler equations in a form particularly suitable for the automatic modeling and on-line control of such mechanisms. The approach is based on Vukobratovic’s method [3], using more conventional Western notation.

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Huang, Y., and C. S. G. Lee. "Generalization of Newton-Euler Formulation of Dynamic Equations to Nonrigid Manipulators." Journal of Dynamic Systems, Measurement, and Control 110, no. 3 (September 1, 1988): 308–15. http://dx.doi.org/10.1115/1.3152687.

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A recursive lumped mass/spring approximation model, based on the Newton-Euler formulation, is proposed to model the dynamics of manipulators with link flexibility. The model assumes that the displacement and rotation due to the link flexibility are measurable. For a small link deformation, a first-order lumped mass/spring approximation model is proposed, in which the parameters of each link are lumped to its joint and the link flexibility is modeled as a spring at each joint. For a larger deformation, the first-order lumped mass/spring approximation model is extended to model each nonrigid link by a series of small rigid segments connected by “pseudo-joints.” The link flexibility is modeled as a spring in each pseudo-joint. In both cases, the effects of torsion and extension are not included in the modeling. An anlaytical error analysis is performed to justify the approximation, and the mathematical relation between the maximum modeling error and the number of pseudo-joints in each link is derived. As the number of pseudo-joints approaches infinity, the joint torques computed by the extended lumped mass/spring approximation model approach the joint torques computed by other models obtained from the Lagrange’s equation.

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Carrillo, José A., and Young-Pil Choi. "Mean-Field Limits: From Particle Descriptions to Macroscopic Equations." Archive for Rational Mechanics and Analysis 241, no. 3 (June 1, 2021): 1529–73. http://dx.doi.org/10.1007/s00205-021-01676-x.

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AbstractWe rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. Crucially, we make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions.

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Xie, Shunqiang. "Kinematic analysis and Newton-Euler equations of a novel hybrid machine tool." Chinese Journal of Mechanical Engineering (English Edition) 15, supp (2002): 132. http://dx.doi.org/10.3901/cjme.2002.supp.132.

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Aslanov, Vladimir, Genrih Kruglov, and Vadim Yudintsev. "Newton–Euler equations of multibody systems with changing structures for space applications." Acta Astronautica 68, no. 11-12 (June 2011): 2080–87. http://dx.doi.org/10.1016/j.actaastro.2010.11.013.

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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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Li, You-Sun, and Anastasios Kessaris. "The Non-Recursive Newton-Euler Formulation of the Dynamic Equation for Robotic Mechanisms." Transactions of the Canadian Society for Mechanical Engineering 10, no. 1 (March 1986): 16–20. http://dx.doi.org/10.1139/tcsme-1986-0003.

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A new formulation of the dynamic equations of an open loop kinematic chain is presented in this paper. This new method is based upon the composite link system concept and the dynamic equations are derived using vectorial analysis. In comparison with conventional methods, the method presented in this paper is more efficient and more explicit, hence it is applicable to both real time control and dynamic computer simulation during the design stage of new robotic mechanisms.

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Brenneis, A., and A. Eberle. "Application of an Implicit Relaxation Method Solving the Euler Equations for Time-Accurate Unsteady Problems." Journal of Fluids Engineering 112, no. 4 (December 1, 1990): 510–20. http://dx.doi.org/10.1115/1.2909436.

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A numerical procedure is presented for computing time-accurate solutions of flows about two and three-dimensional configurations using the Euler equations in conservative form. A nonlinear Newton method is applied to solve the unfactored implicit equations. Relaxation is performed with a point Gauss-Seidel algorithm ensuring a high degree of vectorization by employing the so-called checkerboard scheme. The fundamental feature of the Euler solver is a characteristic variable splitting scheme (Godunov-type averaging procedure, linear locally one-dimensional Riemann solver) based on an eigenvalue analysis for the calculation of the fluxes. The true Jacobians of the fluxes on the right-hand side are used on the left-hand side of the first order in time-discretized Euler equations. A simple matrix conditioning needing only few operations is employed to evade singular behavior of the coefficient matrix. Numerical results are presented for transonic flows about harmonically pitching airfoils and wings. Comparisons with experiments show good agreement except in regions where viscous effects are evident.

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Hao, Xiu Qing. "Inverse Kinematic Solution and Dynamic Model to 3PTT Parallel Mechanism." Advanced Materials Research 945-949 (June 2014): 1421–25. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.1421.

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Take typical parallel mechanism 3PTT as research subject, its inverse kinematic analysis solution was gotten. Dynamic model of the mechanism was established by Newton-Euler method, and the force and torque equations were derived. Dynamic simulation of 3PTT parallel mechanism was done by using ADAMS software, and simulation results have verified the correctness of the theoretical conclusions.

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Hicken, Jason E., and David W. Zingg. "Parallel Newton-Krylov Solver for the Euler equations Discretized Using Simultaneous Approximation Terms." AIAA Journal 46, no. 11 (November 2008): 2773–86. http://dx.doi.org/10.2514/1.34810.

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Shabana, Ahmed A., Mahmoud Tobaa, Brian Marquis, and Magdy El-Sibaie. "Effect of the Linearization of the Kinematic Equations in Railroad Vehicle System Dynamics." Journal of Computational and Nonlinear Dynamics 1, no. 1 (May 5, 2005): 25–34. http://dx.doi.org/10.1115/1.1951783.

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The sensitivity of the wheel/rail contact problem to the approximations made in some of the creepage expressions is examined in this investigation. It is known that railroad vehicle models that employ kinematic linearization can predict, particularly at high speeds, significantly different dynamic response as compared to models that are based on fully nonlinear kinematic and dynamic equations. In order to analytically examine this problem and numerically quantify the effect of the approximations used in the linearized railroad vehicle models, the fully nonlinear kinematic and dynamic equations of a wheel set are presented. The linearized kinematic and dynamic equations used in some railroad vehicle models are obtained from the fully nonlinear model in order to shed light on the assumptions and approximations used in the linearized models. The assumptions of small angles that are often made in developing railroad vehicle models and their effect on the angular velocity, angular acceleration, and the inertia forces are investigated. The velocity creepage expressions that result from the use of the assumptions of small angles are obtained and compared with the fully nonlinear expressions. Newton-Euler equations for the wheel set are presented and their dependence on Euler angles and their time derivatives is discussed. The effect of the linearization assumptions on the form of Newton-Euler equations is examined. A suspended wheel set model is used as an example to obtain the numerical results required to quantify the effect of the linearization. The results obtained in this investigation show that linearization of the creepages can lead to significant errors in the values predicted for the longitudinal and tangential forces as well as the spin moment. There are also significant differences between the two models in the prediction of the lateral and vertical forces used to evaluate the L∕V ratios as demonstrated by the results presented in this investigation.

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Wang, Linkang, Jingjing You, Xiaolong Yang, Huaxin Chen, Chenggang Li, and Hongtao Wu. "Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism." Sensors 21, no. 1 (January 1, 2021): 233. http://dx.doi.org/10.3390/s21010233.

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The solution of the dynamic equations of the six-axis accelerometer is a prerequisite for sensor calibration, structural optimization, and practical application. However, the forward dynamic equations (FDEs) and inverse dynamic equations (IDEs) of this type of system have not been completely solved due to the strongly nonlinear coupling relationship between the inputs and outputs. This article presents a comprehensive study of the FDEs and IDEs of the six-axis accelerometer based on a parallel mechanism. Firstly, two sets of dynamic equations of the sensor are constructed based on the Newton–Euler method in the configuration space. Secondly, based on the analytical solution of the sensor branch chain length, the coordination equation between the output signals of the branch chain is constructed. The FDEs of the sensor are established by combining the coordination equations and two sets of dynamic equations. Furthermore, by introducing generalized momentum and Hamiltonian function and using Legendre transformation, the vibration differential equations (VDEs) of the sensor are derived. The VDEs and Newton–Euler equations constitute the IDEs of the system. Finally, the explicit recursive algorithm for solving the quaternion in the equation is given in the phase space. Then the IDEs are solved by substituting the quaternion into the dynamic equations in the configuration space. The predicted numerical results of the established FDEs and IDEs are verified by comparing with virtual and actual experimental data. The actual experiment shows that the relative errors of the FDEs and the IDEs constructed in this article are 2.21% and 7.65%, respectively. This research provides a new strategy for further improving the practicability of the six-axis accelerometer.

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Liu, Yu, and Yi Lin Wu. "Model-Based Verifying and Design of Autonomous Airship." Applied Mechanics and Materials 66-68 (July 2011): 1748–54. http://dx.doi.org/10.4028/www.scientific.net/amm.66-68.1748.

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Based on the Kirchhoff equations, Newton-Euler laws, boundary layer theory and mass definition, the six degrees of freedom dynamic model of airship complete with aerodynamic forces, wind effect is presented. Then, the nonlinear dynamic model is divided into three group equations by restricting airship motion in different planes respectively. The motion characteristics of airship, including stability, the effect of ballast position and rotational damping, are studied using linearized model. The results of simulation verify the correctness of the theoretical analysis and airship design.

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Mata, V., S. Provenzano, J. L. Cuadrado, and F. Valero. "Inverse dynamic problem in robots using Gibbs-Appell equations." Robotica 20, no. 1 (January 2002): 59–67. http://dx.doi.org/10.1017/s0263574701003502.

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In this paper, two algorithms for solving the Inverse Dynamic Problem based on the Gibbs-Appell equations are proposed and verified. Both are developed using mainly vectorial variables, and the equations are expressed in a recursive form. The first algorithm has a computational complexity of O(n2) and is the least efficient of the two; the second algorithm has a computational complexity of O(n). This algorithm will be compared with one based on Newton-Euler equations of motion, formulated in a similar way, and using mainly vectors in its recursive formulation. The O(n) proposed algorithm will be used to solve the Inverse Dynamic Problem in a PUMA industrial robot.

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Wang, Q., and D. R. Broome. "A new simulation scheme for self-tuning adaptive control of robot manipulators." Robotica 9, no. 3 (July 1991): 335–39. http://dx.doi.org/10.1017/s0263574700006500.

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SUMMARYIn most dynamic adaptive control simulation of robotic manipulators, the Langrange–Euler (L–E) dynamic equations are first piecewise linearized about the desired reference and then discretized and rewritten in a state space form. This makes things very complicated and it is easy to make errors. What is more is that with a different reference this work must be done again. A new simulation scheme – Backward Recursive Self-Tuning Adaptive (BRSTA) – as it will be called, is suggested in this paper for adaptive controller design of robot manipulators. A two degree of freedom robot manipulator is used to verify the scheme in the condition of highly nonlinear and highly coupled system. A one degree of freedom robot manipulator is used for comparing both the forward and backward methods. The main advantages of this scheme include that it can be used for evaluating the self-tuning adaptive control laws and provide the initial process parameters for real-time control. And it is concluded here that the Newton–Euler (N–E) dynamic equations are equally well qualified as the Langrange–Euler (L-E) equations for the simulation of self-tuning adaptive control of robot manipulators.

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Dasgupta, Bhaskar, and T. S. Mruthyunjaya. "Closed-Form Dynamic Equations of the General Stewart Platform through the Newton–Euler Approach." Mechanism and Machine Theory 33, no. 7 (October 1998): 993–1012. http://dx.doi.org/10.1016/s0094-114x(97)00087-6.

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Zahariev, E. V. "Earthquake dynamic response of large flexible multibody systems." Mechanical Sciences 4, no. 1 (February 20, 2013): 131–37. http://dx.doi.org/10.5194/ms-4-131-2013.

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Abstract. In the paper dynamics of large flexible structures imposed on earthquakes and high amplitude vibrations is regarded. Precise dynamic equations of flexible systems are the basis for reliable motion simulation and analysis of loading of the design scheme elements. Generalized Newton–Euler dynamic equations for rigid and flexible bodies are applied. The basement compulsory motion realized because of earthquake or wave propagation is presented in the dynamic equations as reonomic constraints. The dynamic equations, algebraic equations and reonomic constraints compile a system of differential algebraic equations which are transformed to a system of ordinary differential equations with respect to the generalized coordinates and the reactions due to the reonomic constraints. Examples of large flexible structures and wind power generator dynamic analysis are presented.

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Gamarra-Rosado, V. O., and E. A. O. Yuhara. "Dynamic modeling and simulation of a flexible robotic manipulator." Robotica 17, no. 5 (September 1999): 523–28. http://dx.doi.org/10.1017/s0263574799001721.

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This work focuses on the dynamic modeling of a flexible robotic manipulator with two flexible links and two revolute joints, which rotates in the horizontal plane. The dynamic equations are derived using the Newton-Euler formulation and the finite element method, based on elementary beam theory. Computer simulation results are presented to illustrate this study. The dynamic model becomes necessary for use in future design and control applications.

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Hiltebrand, Andreas, and Siddhartha Mishra. "Efficient Preconditioners for a Shock Capturing Space-Time Discontinuous Galerkin Method for Systems of Conservation Laws." Communications in Computational Physics 17, no. 5 (May 2015): 1320–59. http://dx.doi.org/10.4208/cicp.140214.271114a.

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AbstractAn entropy stable fully discrete shock capturing space-time Discontinuous Galerkin (DG) method was proposed in a recent paper to approximate hyperbolic systems of conservation laws. This numerical scheme involves the solution of a very large nonlinear system of algebraic equations, by a Newton-Krylov method, at every time step. In this paper, we design efficient preconditioners for the large, non-symmetric linear system, that needs to be solved at every Newton step. Two sets of preconditioners, one of the block Jacobi and another of the block Gauss-Seidel type are designed. Fourier analysis of the preconditioners reveals their robustness and a large number of numerical experiments are presented to illustrate the gain in efficiency that results from preconditioning. The resulting method is employed to compute approximate solutions of the compressible Euler equations, even for very high CFL numbers.

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Casius, L. J. Richard, Maarten F. Bobbert, and Arthur J. van Soest. "Forward Dynamics of Two-Dimensional Skeletal Models. A Newton-Euler Approach." Journal of Applied Biomechanics 20, no. 4 (November 2004): 421–49. http://dx.doi.org/10.1123/jab.20.4.421.

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Mathematical modeling and computer simulation play an increasingly important role in the search for answers to questions that cannot be addressed experimentally. One of the biggest challenges in forward simulation of the movements of the musculoskeletal system is finding an optimal control strategy. It is not uncommon for this type of optimization problem that the segment dynamics need to be calculated millions of times. In addition, these calculations typically consume a large part of the CPU time during forward movement simulations. As numerous human movements are two-dimensional (2-D) to a reasonable approximation, it is extremely convenient to have a dedicated, computational efficient method for 2-D movements. In this paper we shall present such a method. The main goal is to show that a systematic approach can be adopted which allows for both automatic formulation and solution of the equations of kinematics and dynamics, and to provide some fundamental insight in the mechanical theory behind forward dynamics problems in general. To illustrate matters, we provide for download an example implementation of the main segment dynamics algorithm, as well as a complete implementation of a model of human sprint cycling.

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Zhang, Yu, Li Yang Xie, and Xiao Jin Zhang. "Transverse Vibration Analysis of Euler-Bernoulli Beams Carrying Concentrated Masses with Rotatory Inertia at Both Ends." Advanced Materials Research 118-120 (June 2010): 925–29. http://dx.doi.org/10.4028/www.scientific.net/amr.118-120.925.

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Transverse vibration analysis is presented for Euler-Bernoulli beams carrying concentrated masses and taking into account their rotatory inertia at both ends. The dimensionless eigenfunctions for the problems are first obtained using the differential equations of motion and considering translational and rotatory springs at both ends. A numerical technique, the Newton–Raphson algorithm, is then used to solve vibration eigenfunctions of the beams. Finally, the influences of different non-dimensional parameters on frequencies are discussed.

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Mandailina, Vera, Syaharuddin Syaharuddin, Dewi Pramita, Malik Ibrahim, and Habib Ratu Perwira Negara. "Wilkinson Polynomials: Accuracy Analysis Based on Numerical Methods of the Taylor Series Derivative." Desimal: Jurnal Matematika 3, no. 2 (May 28, 2020): 155–60. http://dx.doi.org/10.24042/djm.v3i2.6134.

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Some of the numeric methods for solutions of non-linear equations are taken from a derivative of the Taylor series, one of which is the Newton-Raphson method. However, this is not the only method for solving cases of non-linear equations. The purpose of the study is to compare the accuracy of several derivative methods of the Taylor series of both single order and two-order derivatives, namely Newton-Raphson method, Halley method, Olver method, Euler method, Chebyshev method, and Newton Midpoint Halley method. This research includes qualitative comparison types, where the simulation results of each method are described based on the comparison results. These six methods are simulated with the Wilkinson equation which is a 20-degree polynomial. The accuracy parameters used are the number of iterations, the roots of the equation, the function value f (x), and the error. Results showed that the Newton Midpoint Halley method was the most accurate method. This result is derived from the test starting point value of 0.5 to the equation root x = 1, completed in 3 iterations with a maximum error of 0.0001. The computational design and simulation of this iterative method which is a derivative of the two-order Taylor series is rarely found in college studies as it still rests on the Newton-Raphson method, so the results of this study can be recommended in future learning.

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Driels, M. R., U. J. Fan, and U. S. Pathre. "The application of newton-euler recursive methods to the derivation of closed form dynamic equations." Journal of Robotic Systems 5, no. 3 (June 1988): 229–48. http://dx.doi.org/10.1002/rob.4620050305.

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Michalak, Christopher, and Carl Ollivier-Gooch. "Globalized matrix-explicit Newton-GMRES for the high-order accurate solution of the Euler equations." Computers & Fluids 39, no. 7 (August 2010): 1156–67. http://dx.doi.org/10.1016/j.compfluid.2010.02.008.

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Yuan, Xinpeng, Jianguo Ning, Tianbao Ma, and Cheng Wang. "Stability of Newton TVD Runge–Kutta scheme for one-dimensional Euler equations with adaptive mesh." Applied Mathematics and Computation 282 (May 2016): 1–16. http://dx.doi.org/10.1016/j.amc.2016.02.006.

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Saha, S. K. "Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices." Journal of Applied Mechanics 66, no. 4 (December 1, 1999): 986–96. http://dx.doi.org/10.1115/1.2791809.

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Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

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CORREC, ANAÏS, and JEAN-PHILIPPE LESSARD. "Coexistence of nontrivial solutions of the one-dimensional Ginzburg-Landau equation: A computer-assisted proof." European Journal of Applied Mathematics 26, no. 1 (October 8, 2014): 33–60. http://dx.doi.org/10.1017/s0956792514000308.

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In this paper, Chebyshev series and rigorous numerics are combined to compute solutions of the Euler-Lagrange equations for the one-dimensional Ginzburg-Landau model of superconductivity. The idea is to recast solutions as fixed points of a Newton-like operator defined on a Banach space of rapidly decaying Chebyshev coefficients. Analytic estimates, the radii polynomials and the contraction mapping theorem are combined to show existence of solutions near numerical approximations. Coexistence of as many as seven nontrivial solutions is proved.

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Miao, Zhonghua, Chenglei Wei, Zhiyuan Gao, and Xuyong Wang. "Active coupling suppression and real-time control system design and implementation for three-axis electronic flight motion simulator." Transactions of the Institute of Measurement and Control 40, no. 4 (February 1, 2017): 1352–61. http://dx.doi.org/10.1177/0142331216683771.

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Modelling of a three-axis electronic flight motion simulator with U-O-O structure is achieved in this paper, based on recursive Newton–Euler equations. To overcome the shortcomings of passive decoupling control methods, an active coupling torque suppression method is proposed using velocity internal feedback by analysing the influence of the coupling torque. Detailed control software and hardware implementation is given for the real-time control system. Experimental tests show the designed flight motion simulator system performs good dynamic and static performances.

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35

Bulyzhenkov, I. E. "Einstein Equation for Nondual Field Matter Modifies Naiver-Stokes Dynamics." International Journal of Modern Physics: Conference Series 47 (January 2018): 1860090. http://dx.doi.org/10.1142/s201019451860090x.

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Cartesian extended matter has its own nondual analog of the 1915 Einstein Equation for pure field physics in nonempty moving space. This tensor balance of energy densities and local stresses leads to Maxwell-type equalities for inertial currents and vector geodesic equations for relativistic accelerations of the Ricci scalar for inertial and gravitational mass densities. Field inertia of slow energy flows reestablishes the living force feedback which is missed in Newton-Euler fluid dynamics and in the Navier-Stokes equation.

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36

Mondejar, F., and A. Vigueras. "The Hamiltonian Dynamics of The Two Gyrostats Problem." International Astronomical Union Colloquium 172 (1999): 303–12. http://dx.doi.org/10.1017/s0252921100072651.

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AbstractThe problem of two gyrostats in a central force field is considered. We prove that the Newton-Euler equations of motion are Hamiltonian with respect to a certain non-canonical structure. The system posseses symmetries. Using them we perform the reduction of the number of degrees of freedom. We show that at every stage of the reduction process, equations of motion are Hamiltonian and give explicit forms corresponding to non-canonical Poissson brackets. Finally, we study the case where one of the gyrostats has null gyrostatic momentum and we study the zero and the second order approximation, showing that all equilibria are unstable in the zero order approximation.

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37

Liu, Guo Jun, Shu Tao Zheng, Peter O. Ogbobe, and Jun Wei Han. "Inverse Kinematic and Dynamic Analyses of the 6-UCU Parallel Manipulator." Applied Mechanics and Materials 127 (October 2011): 172–80. http://dx.doi.org/10.4028/www.scientific.net/amm.127.172.

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From the practical viewpoint, the inverse kinematics and dynamics of a practical Stewart platform, the 6-UCU parallel manipulator, are established in this paper. The velocities and accelerations of the manipulator are derived with the consideration of the attachments of the joints, and then the driving forces actuated by the actuators and the reaction forces applied to the joints are derived based on the Newton Euler method. In the last, the correctness of the equations established in this paper is confirmed by the study of a case. These equations can be used as the base for the precise analysis of the 6-UCU parallel manipulator.

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Wang, L.-P., J.-S. Wang, Y.-W. Li, and Y. Lu. "Kinematic and dynamic equations of a planar parallel manipulator." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 217, no. 5 (May 1, 2003): 525–31. http://dx.doi.org/10.1243/095440603765226812.

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This paper presents an inverse dynamic formulation using the Newton-Euler approach for a planar parallel manipulator, which is used in a new five-axis hybrid machine tool. The inverse kinematics of the manipulator is given and the velocity and the acceleration formulae are derived. The driving forces acting on the legs are determined according to the dynamic formulation. The formulation has been implemented in a program and has been used for some typical trajectories planned for a numerical simulation experiment. The simulation results reveal the nature of the variation of the driving forces in the hybrid machine tool and justify the dynamic control model. The dynamic modelling approach presented in this paper can also be applied to other parallel manipulators with less than six degrees of freedom.

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Hwang, Yunn Lin, Wei Hsin Gau, Wen Huang Lin, Shen Jenn Hwang, and Chien Hsin Chen. "Using Nonlinear Recursive Formulation for the Kinematic Analysis of Human Biomechanical Systems." Advanced Materials Research 482-484 (February 2012): 938–41. http://dx.doi.org/10.4028/www.scientific.net/amr.482-484.938.

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Generally speaking, the human biomechanical systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, the nonlinear recursive formulation is developed for the kinematic analysis of human biomechanical systems. The nonlinear generalized Newton-Euler equations are developed for flexible 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 formulation to solve equations of motion for human biomechanical systems consisting of interconnected rigid and flexible bodies is presented in this paper.

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Kuo, A. D. "A Least-Squares Estimation Approach to Improving the Precision of Inverse Dynamics Computations." Journal of Biomechanical Engineering 120, no. 1 (February 1, 1998): 148–59. http://dx.doi.org/10.1115/1.2834295.

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A least-squares approach to computing inverse dynamics is proposed. The method utilizes equations of motion for a multi-segment body, incorporating terms for ground reaction forces and torques. The resulting system is overdetermined at each point in time, because kinematic and force measurements outnumber unknown torques, and may be solved using weighted least squares to yield estimates of the joint torques and joint angular accelerations that best match measured data. An error analysis makes it possible to predict error magnitudes for both conventional and least-squares methods. A modification of the method also makes it possible to reject constant biases such as those arising from misalignment of force plate and kinematic measurement reference frames. A benchmark case is presented, which demonstrates reductions in joint torque errors on the order of 30 percent compared to the conventional Newton–Euler method, for a wide range of noise levels on measured data. The advantages over the Newton–Euler method include making best use of all available measurements, ability to function when less than a full complement of ground reaction forces is measured, suppression of residual torques acting on the top-most body segment, and the rejection of constant biases in data.

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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 (March 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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El MARAGHY, W. H., H. A. El MARAGHY, and A. IBRAHIM. "BONDGRAPH MODELLING OF ROBOT DYNAMICS." Transactions of the Canadian Society for Mechanical Engineering 13, no. 4 (December 1989): 123–32. http://dx.doi.org/10.1139/tcsme-1989-0019.

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Euler-Lagrange and Newton-Euler dynamic modelling become very involved and the equations quite complex even for a robot of few axes. For robot models, the bondgraph approach provides several advantages such as explicit bondgraph representation of the robot physical parameters and does not involve any complex equation writing or matrix inversion. In this paper, the use of the bondgraph method for modelling and simulating robot dynamics is presented. To illustrate the technique, a dynamic model for a SCARA robot is derived using bondgraph modelling. The causality conflict arising from the dependent inertias is solved by introducing structural and joint damping. Simulation results obtained using the developed model were in very close agreement with the analytical values obtained using the manipulator kinematic relations. Response due to impact excitation was obtained and is presented.

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Uyulan, Çağlar, and Batuhan İpek. "Watt Six-Bar Compliant Mechanism Analysis Based on Kinematic and Dynamic Responses." Scientific Research Communications 1, no. 1 (July 29, 2021): 1–25. http://dx.doi.org/10.52460/src.2021.002.

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In this study, a complete guide to kinematic and kinetic analyses of a Watt type six-bar compliant mechanism is conducted incorporating the flexible buckling of the initially straight element. In the analysis procedure, the hybrid utilization of the pseudo-rigid-body model (PRBM) and the nonlinear elastic theory of beam buckling is presented. This partially compliant mechanism comprises three rigid links and two flexible links. The kinematic analyses of the mechanisms are done by using the vector loop closure equations, the PRBM of a large deflection cantilever beam, and derivation of nonlinear algebraic equations considering the quasi-static equilibrium and load-deflection curve of the flexible parts. Each of the elastic parts makes up a buckling pinned-pinned flexible Euler beam. The vector loop equations are combined with Newton-Euler dynamic formulations to provide the simultaneous constraint matrix. After these operations, the full mechanism is simulated to get both accelerations and forces for each time step. Finally, the design method is validated through experimental results. The findings derived from the combination of buckling elastica solution and PRBM approach enable the analysis of Watt's six-bar compliant mechanism.

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Kozłowski, Krzysztof. "Computational requirements for a discrete Kalman filter in robot dynamics algorithms." Robotica 11, no. 1 (January 1993): 27–36. http://dx.doi.org/10.1017/s0263574700015411.

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SUMMARYIn standard classical kinematic and dynamic considerations the equations of motion for an n-link manipulator can be obtained as recursive Newton-Euler equations. Another approach to finding the inverse dynamics equations is to formulate the system dynamics and kinematics as a two-point boundary-value problem. The equivalence between these two approaches has been proved in this paper. Solution to the two-point boundary-value problem leads to the forward dynamics equations which are similar to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The extensive numerical studies conducted by the author on the new inverse and forward dynamics algorithms derived from the two-point boundary-value problem establish the same level of confidence as exists for current methods. In order to obtain the algorithms with the smallest coefficients of the polynomial of order O(n), the categorization procedure has been implemented in this work.

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Jegen, Marion D., Mark E. Everett, and Adam Schultz. "Using homotopy to invert geophysical data." GEOPHYSICS 66, no. 6 (November 2001): 1749–60. http://dx.doi.org/10.1190/1.1487117.

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Homotopy is a powerful tool for solving nonlinear equations. It is used here to solve small‐dimensional geophysical inverse problems by locating the solutions of the governing normal equations. An Euler‐Newton numerical continuation scheme is used to map trajectories in model space that start from a prescribed solution to a trivial set of equations and terminate at a solution to the inverse problem. The trajectories often map out a continuum of equivalent solutions that are caused by model equivalences or overparameterization. This allows exploration of the solution space topology. The homotopy method, in this application, is relatively insensitive to the choice of starting model. Several examples based on synthetic controlled‐source electromagnetic (CSEM) responses are shown to illustrate the method. An inversion of actual CSEM data from the Canadian Shield is also provided.

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Li, Bo, Xiaoting Rui, Guoping Wang, Jianshu Zhang, and Qinbo Zhou. "On modeling and dynamics of a multiple launch rocket system." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 235, no. 12 (March 10, 2021): 1664–86. http://dx.doi.org/10.1177/0954410020982243.

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Dynamics analysis is currently a key technique to fully understand the dynamic characteristics of sophisticated mechanical systems because it is a prerequisite for dynamic design and control studies. In this study, a dynamics analysis problem for a multiple launch rocket system (MLRS) is developed. We particularly focus on the deductions of equations governing the motion of the MLRS without rockets by using a transfer matrix method for multibody systems and the motion of rockets via the Newton–Euler method. By combining the two equations, the differential equations of the MLRS are obtained. The complete process of the rockets’ ignition, movement in the barrels, airborne flight, and landing is numerically simulated via the Monte Carlo stochastic method. An experiment is implemented to validate the proposed model and the corresponding numerical results.

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Kabuka, M., and R. Escoto. "Real-time implementation of the Newton-Euler equations of motion on the NEC mu PD77230 DSP." IEEE Micro 9, no. 1 (February 1989): 66–76. http://dx.doi.org/10.1109/40.16795.

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Cardall, Christian. "Minkowski and Galilei/Newton Fluid Dynamics: A Geometric 3 + 1 Spacetime Perspective." Fluids 4, no. 1 (December 26, 2018): 1. http://dx.doi.org/10.3390/fluids4010001.

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A kinetic theory of classical particles serves as a unified basis for developing a geometric 3 + 1 spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases on as common a footing as possible reveals that the particle four-momentum is better regarded as comprising momentum and inertia rather than momentum and energy; and, consequently, that the object now known as the stress-energy or energy-momentum tensor is more properly understood as a stress-inertia or inertia-momentum tensor. In dealing with both fiducial and comoving frames as fluid dynamics requires, tensor decompositions in terms of the four-velocities of observers associated with these frames render use of coordinate-free geometric notation not only fully viable, but conceptually simplifying. A particle number four-vector, three-momentum (1, 1) tensor, and kinetic energy four-vector characterize a simple fluid and satisfy balance equations involving spacetime divergences on both Minkowski and Galilei/Newton spacetimes. Reduced to a fully 3 + 1 form, these equations yield the familiar conservative formulations of special relativistic and non-relativistic fluid dynamics as partial differential equations in inertial coordinates, and in geometric form will provide a useful conceptual bridge to arbitrary-Lagrange–Euler and general relativistic formulations.

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Yu, Zheng Ning, Wen Long Li, Peng Shi, and Yu Shan Zhao. "Dynamics of Space Station with Changing Structures." Advanced Materials Research 433-440 (January 2012): 5783–88. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.5783.

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Deploying traditional method for establishing dynamics model of space station is inefficient when the structure of this space station will change. Therefore, a new approach was proposed to obtain general model that suits different structures and configurations. The new method is based on invariant absolute coordinates set and Newton-Euler method. Two simple constraints are firstly described and then used to construct new, more complex ones. While the coordinate set remains the same, main program configuration procedure is executed by including or excluding equations, thus making the model building process more simple. After this, specific equations of motion are being solved. Applying the technique to space stations of different configurations and structures gives good results, and those results are well-agreed with theoretical analysis.

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Tempel, Philipp, Philipp Miermeister, Armin Lechler, and Andreas Pott. "Modelling of Kinematics and Dynamics of the IPAnema 3 Cable Robot for Simulative Analysis." Applied Mechanics and Materials 794 (October 2015): 419–26. http://dx.doi.org/10.4028/www.scientific.net/amm.794.419.

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This paper covers the kinematics and dynamics modelling of the mechatronic model for a 6 DOF cable-driven parallel robot and derives a real-time capable simulation model for such robots. The governing equations of motion for the platform are derived using Newton-Euler formalism, furthermore, the pulley kinematics of the winches and a linear spring-damper based cable model is introduced. Once the equations of motion are derived, closed-form force distribution is implemented and simulation results of the real-time capable model for the cable-driven parallel robot IPAnema3 are presented. Given the real-time capability, the presented model can be used for hardware-in-the-loop simulation or controller design, but also for case studies of highly dynamic or large-scale robots.

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Journal articles on the topic 'Newton-Euler equations'

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