Journal articles: 'Motions (Law)'

1

Peskir, Goran. "On Newton’s First Law of Motion." Axioms 11, no. 7 (June 29, 2022): 319. http://dx.doi.org/10.3390/axioms11070319.

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We present arguments in support of the view that Newton’s first law of motion extends itself to stochastic motions as follows: Every entity perseveres in its state of independent and stationary increments except insofar as it is compelled to change its state by forces impressed. Some of the far-reaching consequences of the extended law are briefly touched upon as well.

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2

XUEJUN, GAO. "BIFURCATION BEHAVIORS OF THE TWO-STATE VARIABLE FRICTION LAW OF A ROCK MASS SYSTEM." International Journal of Bifurcation and Chaos 23, no. 11 (November 2013): 1350184. http://dx.doi.org/10.1142/s0218127413501848.

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Based on the stability and bifurcation theory of dynamical systems, the bifurcation behaviors and chaotic motions of the two-state variable friction law of a rock mass system are investigated by the bifurcation diagrams based on the continuation method and the Poincaré maps. The stick-slip of the rock mass is formulated as an initial values problem for an autonomous system of three coupled nonlinear ordinary differential equations (ODEs) of first order. The results of linear stability analysis indicate that there is an equilibrium position in the rock mass system. Furthermore, numerical results of nonlinear analysis indicate that the equilibrium position loses its stability from a sup-critical Hopf bifurcation point, and then the bifurcating periodic motion evolves into chaotic motion through a series of period-doubling bifurcations with the decreasing of the control parameter. The stick-slip and chaotic motions evolve into infinity in the end with some unstable periodic motions.

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3

Ferland, René, and Gaston Giroux. "Law of Large Numbers for Dynamic Bargaining Markets." Journal of Applied Probability 45, no. 1 (March 2008): 45–54. http://dx.doi.org/10.1239/jap/1208358950.

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We describe the random meeting motion of a finite number of investors in markets with friction as a Markov pure-jump process with interactions. Using a sequence of these, we prove a functional law of large numbers relating the large motions with the finite market of the so-called continuum of agents.

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4

Ferland, René, and Gaston Giroux. "Law of Large Numbers for Dynamic Bargaining Markets." Journal of Applied Probability 45, no. 01 (March 2008): 45–54. http://dx.doi.org/10.1017/s0021900200003946.

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We describe the random meeting motion of a finite number of investors in markets with friction as a Markov pure-jump process with interactions. Using a sequence of these, we prove a functional law of large numbers relating the large motions with the finite market of the so-called continuum of agents.

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5

Nguyen, Thu Dang Thien. "Fick Law and Sticky Brownian Motions." Journal of Statistical Physics 174, no. 2 (November 13, 2018): 494–518. http://dx.doi.org/10.1007/s10955-018-2190-y.

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6

Hamdi, Tarek. "Monotone and boolean unitary Brownian motions." Infinite Dimensional Analysis, Quantum Probability and Related Topics 18, no. 02 (June 2015): 1550012. http://dx.doi.org/10.1142/s0219025715500125.

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The additive monotone (respectively boolean) unitary Brownian motion is a non-commutative stochastic process with monotone (respectively boolean) independent and stationary increments which are distributed according to the arcsine law (respectively Bernoulli law). We introduce the monotone and boolean unitary Brownian motions and derive a closed formula for their associated moments. This provides a description of their spectral measures. We prove that, in the monotone case, the multiplicative analog of the arcsine distribution is absolutely continuous with respect to the Haar measure on the unit circle, whereas in the boolean case the multiplicative analog of the Bernoulli distribution is discrete. Finally, we use quantum stochastic calculus to provide a realization of these processes as the stochastic exponential of the correspending additive Brownian motions.

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Li, Liping, and Albert C. J. Luo. "On Periodic Solutions of a Time-Delayed, Discontinuous System with a Hyperbola Switching Control Law." International Journal of Bifurcation and Chaos 31, no. 02 (February 2021): 2150032. http://dx.doi.org/10.1142/s0218127421500322.

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In this paper, the existence of periodic motions of a discontinuous delayed system with a hyperbolic switching boundary is investigated. From the delay-related [Formula: see text]-function, the crossing, sliding and grazing conditions of a flow to the switching boundary are first developed. For this time-delayed discontinuous dynamical system, there are 17 classes of generic mappings in phase plane and 66 types of local mappings in a delay duration. The generic mappings are determined by subsystems in three domains and two switching boundaries. Periodic motions in such a delay discontinuous system are constructed and predicted analytically from specific mapping structures. Three examples are given for the illustration of periodic motions with or without sliding motion on the switching boundary. This paper shows how to develop switchability conditions of motions at the switching boundary in the time-delayed discontinuous systems and how to construct the specific periodic solutions for the time-delayed discontinuous systems. This study can help us understand complex dynamics in time-delayed discontinuous dynamical systems, and one can use such analysis to control the time-delayed discontinuous dynamical systems.

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Feng, Xiangheng, Yonggang Lin, Guohao Zhang, Danyang Li, Hongwei Liu, and Bin Wang. "Influence of Combined Motion of Pitch and Surge with Phase Difference on Aerodynamic Performance of Floating Offshore Wind Turbine." Journal of Marine Science and Engineering 9, no. 7 (June 25, 2021): 699. http://dx.doi.org/10.3390/jmse9070699.

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Platform motions induced by waves pose a challenge to accurately predict the aerodynamic performance of floating offshore wind turbines (FOWTs). In view of this, the power performance and wake structure of FOWTs under platform pitch, surge, and their combined motions were investigated in this paper, using the computational fluid dynamics software, STAR-CCM+, with overset meshing and rigid body motion techniques. First, the simulation cases in single and same-phase combined motions with different amplitudes and frequencies were performed. Afterward, the approach of calculating the phase difference between pitch and surge motions was proposed to investigate the influence of the combined motion with phase difference on the aerodynamic performance. Results show that the increment of amplitude and frequency augments the mean power output and aggravates the power fluctuation in single and same-phase combined motions. The intensity of power variation under combined motion with a phase difference is weakened at 0.1 Hz compared to the single motion, while enhanced at 0.2 Hz, showing a different influence law on the aerodynamic performance. In addition, this paper established the power fluctuation table based on real sea states of Shidao in China, providing a certain reference for the controller design in this sea area.

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9

Dang, Liem X., Philippe Bopp, and Max Wolfsberg. "Evaluationof Isotope Effectson Henry's Law Constants by a Molecular DynamicsTechnique." Zeitschrift für Naturforschung A 44, no. 5 (May 1, 1989): 485–91. http://dx.doi.org/10.1515/zna-1989-0519.

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Solute isotope effects on Henry’s law constants of aqueous solutions of argon atoms, of helium atoms, and of nitrogen molecules are considered. A cell model is employed; the translational and rotational motions are treated in the first quantum approximation while the vibrational motion of nitrogen is fully treated (but assumed to be separable and harmonic). The required mean square forces (or equivalent frequency parameters) are evaluated by classical molecular dynamics calculations.

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10

Fetecau, Constantin, Dumitru Vieru, Waqas Nazeer, and Shehraz Akhtar. "Long-time solutions for some mixed boundary value problems depicting motions of a class of Maxwell fluids with pressure dependent viscosity." Open Journal of Mathematical Sciences 6, no. 1 (June 21, 2022): 192–204. http://dx.doi.org/10.30538/oms2022.0188.

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Closed-form expressions are established for dimensionless long-tome solutions of some mixed initial-boundary value problems. They correspond to three isothermal unsteady motions of a class of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure. The fluid motion, between infinite horizontal parallel flat plates, is induced by the lower plate that applies time-dependent shear stresses to the fluid. As a check of the obtained results, the similar solutions corresponding to the classical incompressible Maxwell fluids performing same motions are recovered as limiting cases of present solutions. Finally, some characteristics of fluid motion as well as the influence of pressure-viscosity coefficient on the fluid motion are graphically presented and discussed.

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11

Fetecau, Constantin, and Abdul Rauf. ""Permanent solutions for some motions of UCM fluids with power-law dependence of viscosity on the pressure"." Studia Universitatis Babes-Bolyai Matematica 66, no. 1 (March 20, 2021): 197–209. http://dx.doi.org/10.24193/subbmath.2021.1.16.

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Steady motion of two types of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure is analytically studied between infinite horizontal parallel plates when the gravity effects are taken into consideration. Simple and exact expressions are established for the permanent components of starting solutions corresponding to two oscillatory motions induced by the lower plate that oscillates in its plane. Such solutions are very important for the experimentalists who want to eliminate the transients from their experiments. The similar solutions for the simple Couette flow of the same fluids, as well as the permanent solutions corresponding to ordinary incompressible Maxwell fluids performing the same motions, are obtained as limiting cases of general solutions. The convergence of starting solutions to their permanent components as well as the influence of physical parameters on the fluid motion is graphically underlined and discussed.

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12

Coale, David. "Needed Changes in Texas Venue Law." Texas Wesleyan Law Review 1, no. 1 (March 1994): 147–68. http://dx.doi.org/10.37419/twlr.v1.i1.4.

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This paper describes and proposes solutions to three tensions between the Civil Practice and Remedies Code and the Rules of Civil Procedure. Part II sets out the history of the two different bodies of venue law in Texas and explains what happened to them in 1983. Part III recommends that the Code be revised so that a motion to change venue because of prejudice can be filed after the answer. Part IV recommends that the Code should be revised so that live testimony is permissible in a hearing on a motion to change venue because of prejudice. Part V analyzes the treatment of motions to change venue on appeal. It recommends that the Code be revised so that the harmless error rule does not apply when a trial court holds a trial in a prejudiced forum. Part VI summarizes the proposed modifications and explains how they work together to increase efficiency and fairness.

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13

Kaila, Ville R. I., and Arto Annila. "Natural selection for least action." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2099 (July 22, 2008): 3055–70. http://dx.doi.org/10.1098/rspa.2008.0178.

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The second law of thermodynamics is a powerful imperative that has acquired several expressions during the past centuries. Connections between two of its most prominent forms, i.e. the evolutionary principle by natural selection and the principle of least action, are examined. Although no fundamentally new findings are provided, it is illuminating to see how the two principles rationalizing natural motions reconcile to one law. The second law, when written as a differential equation of motion, describes evolution along the steepest descents in energy and, when it is given in its integral form, the motion is pictured to take place along the shortest paths in energy. In general, evolution is a non-Euclidian energy density landscape in flattening motion.

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14

Wang, Yulu, Fahui Zhu, and Yonghui Xie. "Numerical Study on the Effect of Non-Sinusoidal Motion on the Energy Extraction Performance of Parallel Foils." Applied Sciences 9, no. 3 (January 23, 2019): 384. http://dx.doi.org/10.3390/app9030384.

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The effect of non-sinusoidal motion which influences the energy extraction performance of foil is considered in this paper. Two oscillation motions, the combined non-sinusoidal plunging and sinusoidal pitching motion, as well as the combined non-sinusoidal pitching and sinusoidal plunging motion, are selected to investigate the oscillation process of two-dimensional parallel foils numerically. The optimal oscillation motion and average power coefficient at different combined motions are gained. The effects of the plunging motion and pitching motion at different oscillation motions are analyzed, and the evolution law of the foil lift force and vortex field are obtained. It is indicated that the non-sinusoidal motion has a significant influence on energy extraction. When the motion is combined (non-sinusoidal plunging and sinusoidal pitching motion), the best extraction performance is gained at Kh = −0.5. The maximal CPm is 0.375 and the maximal η is 0.188. When the motion is combined (non-sinusoidal pitching and sinusoidal plunging motion), the maximal CPm is 0.623 and the maximal η is 0.312 which appear at Kθ = 2. For the same frequency, the more the plunging motion is similar to the sinusoidal motion, the more energy is extracted by foils. While the more the pitching motion approximates to the square wave, the worse the achieved extraction performance is.

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15

Dai, Hongshuai. "Convergence in Law to Operator Fractional Brownian Motions." Journal of Theoretical Probability 26, no. 3 (January 6, 2012): 676–96. http://dx.doi.org/10.1007/s10959-011-0401-4.

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16

FITRIADHY, AHMAD, and AMIRA ADAM. "CFD ANALYSIS ON VERTICAL MOTION OF A FULL-SCALE FLOATING JETTY." Journal of Sustainability Science and Management 15, no. 6 (August 30, 2020): 100–110. http://dx.doi.org/10.46754/jssm.2020.08.009.

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A floating jetty often experiences several vertical motions i.e., heave and pitch motion responses due to harsh environmental condition. This inherently makes discomfort to everyone during berthing on a floating; and even it potentially leads to loss of life due to falling down into the sea. A preliminary analysis using Computational Fluid Dynamics (CFD) simulation is necessary to be conducted to ensure user’s safety. The CFD analysis focused on the interaction between wave motions and the floating jetty and its effects on the vertical motions. The vertical motions of floating jetty were quantified by the Response Amplitude Operators (RAO). Several effects due to variation of wavelength (λ/L) have been studied. The CFD results revealed that the lower wavelength (λ/L<2.25) resulted in the increase of the heave and pitch motion amplitudes proportionally. However, the subsequent increase of wavelength (2.25>λ/L) has given results to less heave and pitch motion amplitudes. In general, it is shown that the vertical motion characteristics of the floating jetty predominantly depend on wave properties.

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17

Yan, Bowen, Yiqian Wang, and Chaoqun Liu. "Liutex-Represented Vortex Spectrum in Turbulence." Entropy 25, no. 1 (December 23, 2022): 25. http://dx.doi.org/10.3390/e25010025.

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The Liutex vector is new quantity introduced to represent the rigid-body rotation part of fluid motion and thus to define and identify vortices in various flows. In this work, the intermittency and power-law similarity of the Liutex vector in homogeneous, isotropic turbulence and a turbulent channel are explored. First, we found that the Liutex vector is more intermittent than the vorticity vector in the considered turbulent flows, which indicates that an iso-surface of a Liutex magnitude with an appropriate threshold could capture the major rotating motions or vortical motions of the flow. Second, the three-dimensional energy spectrums of velocity, vorticity (enstrophy spectrum) and the Liutex vector in homogeneous isotropic turbulence are shown to exhibit power laws of −5/3, 1/3 and 1/3 in the inertial subrange, respectively, whilst the Liutex energy spectrum particularly satisfies an additional −10/3 power law in the viscous subrange. This viscous similarity of the Liutex vector is the only power law that survived from the wall presence and is argued to originate from the fact that the Liutex vector represents the rigid part of fluid motion and is free from any shear contamination. The existence of such a viscous similarity law indicates a certain coherence of the small scales of turbulence and could possibly help understand and model turbulence.

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18

Orsingher, Enzo. "Random motions governed by third-order equations." Advances in Applied Probability 22, no. 4 (December 1990): 915–28. http://dx.doi.org/10.2307/1427568.

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In this paper we analyse the motion of a particle P whose velocity is represented by a three-valued telegraph process. We prove that the probability law of the process describing the position of P is a solution of a third-order, linear, partial differential equation.We obtain probability distributions of some generalised versions of the process of random signals, as well as other probabilistic features of the related process.Finally, accelerated motions of P (where acceleration follows the classical telegraph process) are also analysed.

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19

Dufresne, Daniel. "The integral of geometric Brownian motion." Advances in Applied Probability 33, no. 1 (March 2001): 223–41. http://dx.doi.org/10.1017/s0001867800010715.

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This paper is about the probability law of the integral of geometric Brownian motion over a finite time interval. A partial differential equation is derived for the Laplace transform of the law of the reciprocal integral, and is shown to yield an expression for the density of the distribution. This expression has some advantages over the ones obtained previously, at least when the normalized drift of the Brownian motion is a non-negative integer. Bougerol's identity and a relationship between Brownian motions with opposite drifts may also be seen to be special cases of these results.

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Orsingher, Enzo. "Random motions governed by third-order equations." Advances in Applied Probability 22, no. 04 (December 1990): 915–28. http://dx.doi.org/10.1017/s0001867800023193.

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In this paper we analyse the motion of a particle P whose velocity is represented by a three-valued telegraph process. We prove that the probability law of the process describing the position of P is a solution of a third-order, linear, partial differential equation. We obtain probability distributions of some generalised versions of the process of random signals, as well as other probabilistic features of the related process. Finally, accelerated motions of P (where acceleration follows the classical telegraph process) are also analysed.

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21

FitzGerald, Will, and Jon Warren. "Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions." Probability Theory and Related Fields 178, no. 1-2 (April 17, 2020): 121–71. http://dx.doi.org/10.1007/s00440-020-00972-z.

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Abstract This paper proves an equality in law between the invariant measure of a reflected system of Brownian motions and a vector of point-to-line last passage percolation times in a discrete random environment. A consequence describes the distribution of the all-time supremum of Dyson Brownian motion with drift. A finite temperature version relates the point-to-line partition functions of two directed polymers, with an inverse-gamma and a Brownian environment, and generalises Dufresne’s identity. Our proof introduces an interacting system of Brownian motions with an invariant measure given by a field of point-to-line log partition functions for the log-gamma polymer.

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Ting, Edward C., Chiang Shih, and Yeon-Kang Wang. "Fundamentals of a Vector Form Intrinsic Finite Element: Part I. Basic Procedure and A Plane Frame Element." Journal of Mechanics 20, no. 2 (June 2004): 113–22. http://dx.doi.org/10.1017/s1727719100003336.

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AbstractIn a series of three articles, fundamentals of a vector form intrinsic finite element procedure (VFIFE) are summarized. The procedure is designed to calculate motions of a system of rigid and deformable bodies. The motion may include large rigid body motions and large geometrical changes. Newton's law, or a work principle, for particle is assumed to derive the governing equations of motion. They are obtained by using a set of deformation coordinates for the description of kinematics. A convected material frame approach is proposed to handle very large deformations. Numerical results are calculated by using an explicit algorithm. In the first article, using the plane frame element as an example, basic procedures are described. In the accompanied articles, plane solid elements, convected material frame procedures and numerical results of patch tests are given.

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23

Iida, Hiroyuki, and Mohd Nor Akmal Khalid. "Using Games to Study Law of Motions in Mind." IEEE Access 8 (2020): 138701–9. http://dx.doi.org/10.1109/access.2020.3012597.

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Tothong, Polsak, C. Allin Cornell, and J. W. Baker. "Explicit Directivity-Pulse Inclusion in Probabilistic Seismic Hazard Analysis." Earthquake Spectra 23, no. 4 (November 2007): 867–91. http://dx.doi.org/10.1193/1.2790487.

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Probabilistic seismic hazard analysis (PSHA) is widely used to estimate the ground motion intensity that should be considered when assessing a structure's performance. Disaggregation of PSHA is often used to identify representative ground motions in terms of magnitude and distance for structural analysis. Forward directivity–induced velocity pulses, which may occur in near-fault (or near-source) motions, are known to cause relatively severe elastic and inelastic response in structures of certain periods. Here, the principles of PSHA are extended to incorporate the possible occurrence of a velocity pulse in a near-fault ground motion. For each magnitude and site-source geometry, the probability of occurrence of a pulse is considered along with the probability distribution of the pulse period given that a pulse does occur. A near-source “narrowband” attenuation law modification to predict ground motion spectral acceleration ( Sa) amplitude that takes advantage of this additional pulse period information is utilized. Further, disaggregation results provide the probability that a given level of ground motion intensity is caused by a pulse-like ground motion, as well as the conditional probability distribution of the pulse period associated with that ground motion. These extensions improve the accuracy of PSHA for sites located near faults, as well as provide a rational basis for selecting appropriate near-fault ground motions to be used in the dynamic analyses of a structure.

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Fan, Jinjun, Ping Liu, Tianyi Liu, Shan Xue, and Zhaoxia Yang. "Analysis of Discontinuous Dynamical Behaviors of a Friction-Induced Oscillator with an Elliptic Control Law." Mathematical Problems in Engineering 2018 (2018): 1–33. http://dx.doi.org/10.1155/2018/5301747.

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This paper develops the passability conditions of flow to the discontinuous boundary and the sticking or sliding and grazing conditions to the separation boundary in the discontinuous dynamical system of a friction-induced oscillator with an elliptic control law and the friction force acting on the mass M through the analysis of the corresponding vector fields and G-functions. The periodic motions of such a discontinuous system are predicted analytically through the mapping structure. Finally, the numerical simulations are given to illustrate the analytical results of motion for a better understanding of physics of motion in the mass-spring-damper oscillator.

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Fetecau, Constantin, Dumitru Vieru, Abdul Rauf, and Tahir Mushtaq Qureshi. "STEADY-STATE SOLUTIONS FOR SOME MOTIONS OF MAXWELL FLUIDS WITH PRESSURE-DEPENDENCE OF VISCOSITY." Journal of Mathematical Sciences: Advances and Applications 68, no. 1 (November 30, 2021): 1–28. http://dx.doi.org/10.18642/jmsaa_7100122224.

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Two isothermal motions of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure are investigated when gravity effects are taken into account. The fluid motion, between two infinite horizontal parallel plates, is generated by the lower plate that applies a time-dependent shear stress to the fluid. Exact expressions are established for the steady-state components of the dimensionless start-up velocity, shear stress, and normal stress. They are used to find the needed time to touch the steady-state and to provide corresponding solutions for the motion of the same fluids induced by an exponential shear stress on the boundary. This time is useful for experimentalists who want to eliminate transients from their experiments. It is higher for motions of ordinary fluids as compared to fluids with pressure-dependent viscosity. The variation of starting solutions (numerical solutions) in time and space is graphically represented and some characteristics of the fluid motion are brought to light.

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De Gregorio, Alessandro. "Stochastic velocity motions and processes with random time." Advances in Applied Probability 42, no. 4 (December 2010): 1028–56. http://dx.doi.org/10.1239/aap/1293113150.

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The aim of this paper is to analyze a class of random processes which models the motion of a particle on the real line with random velocity and subject to the action of friction. The speed randomly changes when a Poissonian event occurs. We study the characteristic and moment generating functions of the position reached by the particle at time t > 0. We are able to derive the explicit probability distributions in a few cases. The moments are also widely analyzed. For the random motions having an explicit density law, further interesting probabilistic interpretations emerge if we consider randomly varying time. Essentially, we consider two different types of random time, namely Bessel and gamma times, which contain, as particular cases, some important probability distributions (e.g. Gaussian, exponential). For the random processes built by means of these compositions, we derive the probability distributions for a fixed number of Poisson events. Some remarks on possible extensions to random motions in higher spaces are proposed. We focus our attention on the persistent planar random motion.

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De Gregorio, Alessandro. "Stochastic velocity motions and processes with random time." Advances in Applied Probability 42, no. 04 (December 2010): 1028–56. http://dx.doi.org/10.1017/s0001867800004511.

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The aim of this paper is to analyze a class of random processes which models the motion of a particle on the real line with random velocity and subject to the action of friction. The speed randomly changes when a Poissonian event occurs. We study the characteristic and moment generating functions of the position reached by the particle at timet> 0. We are able to derive the explicit probability distributions in a few cases. The moments are also widely analyzed. For the random motions having an explicit density law, further interesting probabilistic interpretations emerge if we consider randomly varying time. Essentially, we consider two different types of random time, namely Bessel and gamma times, which contain, as particular cases, some important probability distributions (e.g. Gaussian, exponential). For the random processes built by means of these compositions, we derive the probability distributions for a fixed number of Poisson events. Some remarks on possible extensions to random motions in higher spaces are proposed. We focus our attention on the persistent planar random motion.

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Stepanenko, Y. "Modal Control of Fast Large-Scale Robot Motions." Journal of Dynamic Systems, Measurement, and Control 109, no. 2 (June 1, 1987): 80–87. http://dx.doi.org/10.1115/1.3143841.

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This study concentrates on the following topics in linear state-feedback robotic control: an algorithm for the generation of linearized robot models, a control law providing a desired eigenstructure for the linearized models, and the eigenvalue sensitivity to changes of the linearized model parameters. The algorithm allows the computer generation of linearized dynamic models for any articulated mechanism with revolute or prismatic joints. It does not include numerical differentiation and is based on a compound-vector technique and Newton-Euler dynamics. The control law allows the arbitrary assignment of all eigenvalues and certain entries of the closed-loop eigenvectors. The general structure of the closed-loop modal matrix and the flexibility available in eigenvector assignment are considered. A sensitivity analysis is given for the decoupled control law resulting from a particular eigenvector assignment. An experimental vertion of the developed modal controller was implemented on a multiprocessor system based on Motorola 68020 microprocessors. Details of the implementation and results of robot motion simulation are also included.

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Sidón-Ayala, Miguel, Javier Pliego-Jiménez, and César Cruz-Hernandez. "Attitude Synchronization of a Group of Rigid Bodies Using Exponential Coordinates." Entropy 25, no. 6 (May 23, 2023): 832. http://dx.doi.org/10.3390/e25060832.

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Currently, managing a group of satellites or robot manipulators requires coordinating their motion and work in a cooperative way to complete complex tasks. The attitude motion coordination and synchronization problems are challenging since attitude motion evolves in non-Euclidean spaces. Moreover, the equation of motions of the rigid body are highly nonlinear. This paper studies the attitude synchronization problem of a group of fully actuated rigid bodies over a directed communication topology. To design the synchronization control law, we exploit the cascade structure of the rigid body’s kinematic and dynamic models. First, we propose a kinematic control law that induces attitude synchronization. As a second step, an angular velocity-tracking control law is designed for the dynamic subsystem. We use the exponential coordinates of rotation to describe the body’s attitude. Such coordinates are a natural and minimal parametrization of rotation matrices which almost describe every rotation on the Special Orthogonal group SO(3). We provide simulation results to show the performance of the proposed synchronization controller.

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Qing, Xue. "Going Through the Motions." Chinese Law & Government 21, no. 3 (October 1988): 96–97. http://dx.doi.org/10.2753/clg0009-4609210396.

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Lee, Ho-Hoon. "A New Motion-Planning Scheme for Overhead Cranes With High-Speed Hoisting." Journal of Dynamic Systems, Measurement, and Control 126, no. 2 (June 1, 2004): 359–64. http://dx.doi.org/10.1115/1.1767855.

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This paper proposes a motion-planning method for a high-performance anti-swing control of overhead cranes, where the motion-planning problem is solved as a kinematic problem. First, an anti-swing regulating control law is proposed based on the Lyapunov stability theorem, where the proposed anti-swing control drives trolley velocity regulating error asymptotically to zero while suppressing load swing rapidly to zero for given arbitrary high-speed hoisting motions. Then a motion-planning scheme is designed based on the concept of minimumtime control, the proposed anti-swing control law, and typical anti-swing crane-operation practices. The motion-planning scheme is free from the usual mathematical constraints in anti-swing control such as small swing angle, small hoisting speed, and small hoisting distance. The effectiveness of the proposed motion planning is shown by generating high-performance anti-swing trajectories with high hoisting speed and hoisting ratio.

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Galloway, Kevin S., and Biswadip Dey. "Beacon-referenced pursuit for collective motions in three dimensions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2234 (February 2020): 20190585. http://dx.doi.org/10.1098/rspa.2019.0585.

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Motivated by real-world applications of unmanned aerial vehicles, this paper introduces a decentralized control mechanism to guide steering control of autonomous agents manoeuvring in the vicinity of multiple moving entities (e.g. other autonomous agents) and stationary entities (e.g. fixed beacons or points of reference) in a three-dimensional environment. The proposed control law, which can be perceived as a modification of the three-dimensional constant bearing (CB) pursuit law, provides a means to allocate simultaneous attention to multiple entities. We investigate the behaviour of the closed-loop dynamics for a system with one agent referencing two beacons, as well as a two-agent mutual pursuit system wherein each agent employs the beacon-referenced CB pursuit law with regards to the other agent and a stationary beacon. Under certain assumptions on the associated control parameters, we demonstrate that this problem admits circling equilibria with agents moving on circular orbits with a common radius, in planes perpendicular to a common axis passing through the beacons. As the common radius and distances from the beacon are determined by the choice of parameters in the pursuit law, this approach provides a means to engineer desired formations in a three-dimensional setting.

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Choi, Stephen J. "Motions for Lead Plaintiff in Securities Class Actions." Journal of Legal Studies 40, no. 1 (January 2011): 205–44. http://dx.doi.org/10.1086/658405.

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Donahue, William H. "Kepler's invention of the second planetary law." British Journal for the History of Science 27, no. 1 (March 1994): 89–102. http://dx.doi.org/10.1017/s000708740003168x.

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Kepler saw it as one of the chief advantages of the Copernican system that it put order into the planetary motions. Although Copernicus had indeed noted that the planetary periods increase with their distance from the sun, he did not, as far as we know, attempt to find a relationship between the two. Believing that God would not have failed to establish some mathematically precise ratio, Kepler sought from the very first to find it. Thus we see, in some of his earliest surviving letters, his attempts to relate planetary periods to the radii of their orbits using circular quadrants intersected by straight lines. Right from the beginning, Kepler gave the sun that dynamic role that was to characterize his ‘new astronomy based upon physics’. Immediately after describing the nested polyhedra that he believed determined the number and distances of the planets, he wrote:Next, there is a moving soul and an infinite motion in the sun, and a double decrement of motion in the movables. In the first place, there is the inequality of their circuits, caused by the unequal amplitude of the orbs, which would occur even were the moving power the same in all orbs. But (2) actually this moving power (like light, in optics) is weaker the further it is from the source.

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36

Iorio, Lorenzo. "Orbital Motions and the Conservation-Law/Preferred-Frame α3 Parameter." Galaxies 2, no. 4 (September 29, 2014): 482–95. http://dx.doi.org/10.3390/galaxies2040482.

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Vielsack, P., and H. Spiess. "Sliding of a Mass on an Inclined Driven Plane With Randomly Varying Coefficient of Friction." Journal of Applied Mechanics 67, no. 1 (July 9, 1999): 112–16. http://dx.doi.org/10.1115/1.321165.

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Investigated are sliding motions of a rigid body on a harmonically driven inclined plane. Coulomb’s law with a random coefficient of friction is assumed. The mean sliding velocity in a steady state of deterministic motions is taken as a measure to compare deterministic with stochastic behavior. Not only do the random parameters influence the deviation in the results but strongly influence the typical features of the different motions themselves. [S0021-8936(00)01701-3]

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Takenaka, Shigeo. "Integral-geometric construction of self-similar stable processes." Nagoya Mathematical Journal 123 (September 1991): 1–12. http://dx.doi.org/10.1017/s0027763000003627.

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Recently, fractional Brownian motions are widely used to describe complex phenomena in several fields of natural science. In the terminology of probability theory the fractional Brownian motion is a Gaussian process {X(t) : t є R} with stationary increments which has a self-similar property, that is, there exists a constant H (for the Brownian motion H = 1/2, in general 0 < H < 1 for Gaussian processes) called the exponent of self-similarity of the process, such that, for any c > 0, two processes are subject to the same law (see [10]).

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Cang, Yuquan, Junfeng Liu, and Yan Zhang. "Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus." Abstract and Applied Analysis 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/635917.

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We study the asymptotic behavior of the sequenceSn=∑i=0n-1K(nαSiH1)(Si+1H2-SiH2),asntends to infinity, whereSH1andSH2are two independent subfractional Brownian motions with indicesH1andH2, respectively.Kis a kernel function and the bandwidth parameterαsatisfies some hypotheses in terms ofH1andH2. Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motionSH1. We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.

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Tang, Yangyang, Yingmin Li, Zongming Huang, Liping Liu, Yishun Ding, and Hui Zhu. "ANALYSIS OF LOCAL SITE EFFECTS ON SEISMIC RESPONSE OF FRAME STRUCTURES SUPPORTED BY FOUNDATIONS AT DIFFERENT ELEVATIONS." NED University Journal of Research 3, Special Issue on First SACEE'19 (December 12, 2019): 181–90. http://dx.doi.org/10.35453/nedjr-stmech-2019-0038.

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Frame structures supported by foundations with different elevations (such as a structure on the slope) undergo different ground motions because of the local site effect. Seismic response of the structure under non-uniform excitation of ground motion is different from that under uniform excitation on upper embedding end or lower embedding end. Sites with the same height difference and different soil conditions were set up in this paper to subject them to ground motions related to different positions and the seismic response of structures built on the sites under uniform and non-uniform strong seismic excitation were compared. The results show that the predominant period and amplitude of ground motions on upper embedding end and lower embedding end are different and affected by soil conditions. The extent and law of amplification of shear force, displacement and storey drift of structures under non-uniform excitation differ from those under uniform excitation when soil changes from soft to medium-hard soil. In addition, the position and degree of plastic hinges change under non-uniform excitation compared to uniform excitation. The uniform excitation using the ground motion on the upper embedding end is not always safe for the frame structure supported by foundations at different elevations.

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Liang, Hao Fang, and Guo Yong Shan. "The Control Method for Positioning Bed of the Body Gamma Knife Based on the Breathing Sensors." Applied Mechanics and Materials 138-139 (November 2011): 560–65. http://dx.doi.org/10.4028/www.scientific.net/amm.138-139.560.

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Objective: To counteract the organ motion caused by respiratory movement through controlling the positioning bed’s synchronous motion with the organ with the breathing sensor in body gamma knife treatment. Methods: The displacement curve of relationship between lung volume and organs in the lung was obtained by acquiring respiratory signals with the piezoelectric film respiratory sensor. Used single chip microcomputer to control stepper motor which spurts the positioning bed through the transmitter to make it move simultaneously in real time according to the law of organ motion, so as to counteract the organ motion caused by respiratory movement and thus to improve the precision of radiotherapy. Results: The experiment indicates that this method can make the steeper motor move according to the displacement curve. Conclusion: It is feasible to counteract the organ and tissue motions caused by respiratory movement by making the positioning bed reversely move in real time in accordance with the law of organ motion during radiotherapy treatment.

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Yin, Fengwei, Guanwei Luo, and Xueming Wang. "Diversity and Regularity of Periodic Impact Motions of a Mechanical Vibration System with Multiple Rigid Stops." Shock and Vibration 2021 (February 11, 2021): 1–21. http://dx.doi.org/10.1155/2021/6624205.

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The mechanical model of a two-degree-of-freedom vibration system with multiple rigid stops was established, and the effects of the multiple rigid stops to dynamic characteristics of two mass blocks of the system were studied. The judgment conditions and differential equations of motion of the system masses impacting rigid stops were analyzed. Based on the multiparameter and multiobjective collaborative simulation analysis, the correlation between the dynamic characteristics of the vibration system and the model parameters is studied. The basic periodic and subharmonic impact motions are analyzed with emphasis on the influences of dynamical parameters on the mode diversity and the distribution characteristics, and the law of emergence and competition of various periodic impact motions on the parametric plane is revealed. The singular points, the hysteresis transition domains, and the accompanying codimension-two bifurcations, caused by the irreversibility of the transition between adjacent basic periodic impact motions in the low-frequency domain, are analyzed. The reasonable parameter matching range, associated with dynamic characteristic optimization of the system, is determined.

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Stalljann, Sarah, Lukas Wöhle, Jeroen Schäfer, and Marion Gebhard. "Performance Analysis of a Head and Eye Motion-Based Control Interface for Assistive Robots." Sensors 20, no. 24 (December 14, 2020): 7162. http://dx.doi.org/10.3390/s20247162.

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Assistive robots support people with limited mobility in their everyday life activities and work. However, most of the assistive systems and technologies for supporting eating and drinking require a residual mobility in arms or hands. For people without residual mobility, different hands-free controls have been developed. For hands-free control, the combination of different modalities can lead to great advantages and improved control. The novelty of this work is a new concept to control a robot using a combination of head and eye motions. The control unit is a mobile, compact and low-cost multimodal sensor system. A Magnetic Angular Rate Gravity (MARG)-sensor is used to detect head motion and an eye tracker enables the system to capture the user’s gaze. To analyze the performance of the two modalities, an experimental evaluation with ten able-bodied subjects and one subject with tetraplegia was performed. To assess discrete control (event-based control), a button activation task was performed. To assess two-dimensional continuous cursor control, a Fitts’s Law task was performed. The usability study was related to a use-case scenario with a collaborative robot assisting a drinking action. The results of the able-bodied subjects show no significant difference between eye motions and head motions for the activation time of the buttons and the throughput, while, using the eye tracker in the Fitts’s Law task, the error rate was significantly higher. The subject with tetraplegia showed slightly better performance for button activation when using the eye tracker. In the use-case, all subjects were able to use the control unit successfully to support the drinking action. Due to the limited head motion of the subject with tetraplegia, button activation with the eye tracker was slightly faster than with the MARG-sensor. A further study with more subjects with tetraplegia is planned, in order to verify these results.

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Rodríguez, L. F. "Orbital Motions in Binary Protostellar Systems." International Astronomical Union Colloquium 191 (August 2004): 92–99. http://dx.doi.org/10.1017/s0252921100008551.

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AbstractUsing high-resolution (~ 01), multi-epoch Very Large Array observations, we have detected orbital motions in several low-luminosity protobinary systems in the Taurus and ρ Ophiuchus molecular complexes. The masses obtained from Kepler’s third law are of the order of 0.5 to 2 M⊙, as expected for such low-mass protostars. The relatively large bolometric luminosities of these young systems corroborates the notion that protostars obtain most of their luminosity from accretion and not from nuclear reactions. In addition, in one of the sources studied (a multiple system in Taurus), a low-mass young star has shown a drastic change in its orbit after a close approach with another component of the system, presumed to be a double star. The large proper motion achieved by this low mass protostar (20 km s−1), suggests an ejection from the system.

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Odrowąż-Sypniewski, Wojciech. "Tryb postępowania z wniesionym w VIII kadencji wnioskiem o wyrażenie przez Sejm zgody na pociągnięcie do odpowiedzialności cywilnej posłów." Zeszyty Prawnicze Biura Analiz Sejmowych 4, no. 68 (2020): 187–99. http://dx.doi.org/10.31268/zpbas.2020.84.

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The author indicates that the legal structure of the Polish immunity regulations excludes the possibility of adopting a resolution by the Sejm on giving consent to bring several deputies to responsibility. In each individual case, the Sejm should consider a separate motion and adopt a separate resolution. Referring to the principle of discontinuity, the author concludes that regarding the two former Deputies, new motions for consent to bring them to a civil law liability should be submitted, while in the case of a Deputy holding a mandate also in the 9th term, the proceedings on the motion concerning him should be continued.

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Wang, Xiaojun, and Jing Lv. "Modeling and simulation of dynamics of a planar-motion rigid body with friction and surface contact." International Journal of Modern Physics B 31, no. 16-19 (July 26, 2017): 1744021. http://dx.doi.org/10.1142/s0217979217440210.

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The modeling and numerical method for the dynamics of a planar-motion rigid body with frictional contact between plane surfaces were presented based on the theory of contact mechanics and the algorithm of linear complementarity problem (LCP). The Coulomb’s dry friction model is adopted as the friction law, and the normal contact forces are expressed as functions of the local deformations and their speeds in contact bodies. The dynamic equations of the rigid body are obtained by the Lagrange equation. The transition problem of stick-slip motions between contact surfaces is formulated and solved as LCP through establishing the complementary conditions of the friction law. Finally, a numerical example is presented as an example to show the application.

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Xi, Ke, Chao Yan, Yu Huang, and Wen Wang. "Coupled CFD/GNC Modeling for the Basic Finner Projectile with Closed Loop." Applied Mechanics and Materials 541-542 (March 2014): 1478–82. http://dx.doi.org/10.4028/www.scientific.net/amm.541-542.1478.

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The virtual flight simulation of the Basic Finner projectile has been investigated through coupling solving unsteady Navier-Stokes equations, rigid-body six degree-of-freedom motion equations, guidance, navigation and control law. The flow solver uses a finite-volume method based on structure grid with dual time stepping, the chimera method is used to simulate relative motions, the fourth-order Runger-Kutta method is used to solve the motion equations. A closed loop feedback control law with PID control is required for the elevator to attain the commanded deflection. The predictions show that the PID parameters for the controller must be correctly selected to obtain the proper response. Simulation results show that the virtual flight simulation platform that we developed is capable of solving the complicated unsteady flows with moving boundary, has a strong applicability to engineering application.

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Lian-zhou, Wang, Guo Chun-yu, Wan Lei, and Su Yu-min. "Numerical Analysis of Propeller During Heave Motion Near a Free Surface." Marine Technology Society Journal 51, no. 1 (January 1, 2017): 40–51. http://dx.doi.org/10.4031/mtsj.51.1.5.

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AbstractThe interaction between the free surface and the propeller during heave motion near the free surface was analyzed numerically using the Reynolds-Averaged Navier-Stokes (RANS) method. The coupling effect between the rotation and heave motions of the propeller was modeled using a motion equation developed in this study; the heave motion was simplified as a periodic motion based on the sinusoidal motion law; and the transfer of numerical values for unsteady flow fields was implemented using overset grid technology. A comparative analysis of the unsteady thrust coefficient and torque coefficient under different advance coefficient conditions was conducted, and the air ingestion phenomenon of the propeller was analyzed. The research highlighted the interaction between the coupled heave and rotation motions of the propeller and the free surface. The results showed that, when the advance coefficient was low, the hydrodynamic performance of the propeller during heave motion near a free surface was strongly influenced by the free surface and that a remarkable interaction existed between the propeller and the free surface. As the advance coefficient increased, the interaction between the propeller and the free surface weakened. The air ingestion that the propeller exerts upon the free surface during heave motion is a complex coupled superposition process. This phenomenon is correlated to the motion state and working time of the propeller, as well as the distance between the propeller and the free surface.

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Yang, Yan, and Guanwei Luo. "Effects of Differently Located Clearance on the Dynamic Responses of a Two-Degree-of-Freedom Vibration System." Shock and Vibration 2021 (September 30, 2021): 1–18. http://dx.doi.org/10.1155/2021/1795675.

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The mechanical model of a two-degree-of-freedom forced harmonic vibration system with multiclearance rigid constraints is established, considering the location schemes of symmetrical both-sided clearance and asymmetrical multiple clearance. Existence domains, correlative distributions, and bifurcation scenarios of periodic vibrations are analyzed using multiparameter and multiperformance cosimulation. Pattern diversity, distribution, and occurrence mechanism of the subharmonic impact motion sequences in the tongue-shaped transition regions among the neighboring fundamental periodic motions of the vibration systems are investigated. The emergent behavior of sticking process of fundamental periodic vibration, the occurrence law of chattering-impact motion, and the interaction of different modes of sticking are discussed. According to the sampling ranges of parameters, three multiple heterogeneous constraint conditions are explored; the effects of differently clearance location and values on the dynamic responses and the transition region of fundamental periodic vibrations and subharmonic motions are particularly analyzed. Hence, the reasonable clearance arrangement scheme and numerical optimization combination are determined and the ideal parameter domain of the vibration system is obtained.

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Nguyen, Choi, and Lee. "Robust Adaptive Heading Control for a Ray-Type Hybrid Underwater Glider with Propellers." Journal of Marine Science and Engineering 7, no. 10 (October 11, 2019): 363. http://dx.doi.org/10.3390/jmse7100363.

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This paper presents the modeling of a new ray-type hybrid underwater glider (RHUG) and an experimental approach used to robustly and adaptively control heading motion. The motions of the proposed RHUG are divided into vertical-plane motions and heading motion. Hydrodynamic coefficients in the vertical-plane dynamics are obtained using a computational fluid dynamics (CFD) method for various pitch angles. Due to the difficulty of obtaining accurate parameter values for the heading dynamics, a robust adaptive control algorithm was designed containing an adaptation law for the unknown parameters and robust action for minimizing environmental disturbances. For robust action against bounded disturbances, such as waves and ocean currents, sliding mode control was applied under the assumption that the bounds of the external disturbances are known. A direct adaptive algorithm for heading motion was applied in an experiment. Computer simulations of the proposed robust adaptive heading control are presented to demonstrate the robustness of the proposed control system in the presence of bounded disturbances. To verify the performance of the proposed controller for heading dynamics, several heading control experiments were conducted in a water tank and in the sea.

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Journal articles on the topic 'Motions (Law)'

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