Relevant bibliographies by topics / Symmetric rigid body

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Symmetric rigid body'

Author: Grafiati
Published: 14 March 2023

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Journal articles on the topic "Symmetric rigid body"

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Dragović, Vladimir, Borislav Gajić, and Božidar Jovanović. "Note on free symmetric rigid body motion." Regular and Chaotic Dynamics 20, no. 3 (May 2015): 293–308. http://dx.doi.org/10.1134/s1560354715030065.

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Celledoni, E., and N. Säfström. "A symmetric splitting method for rigid body dynamics." Modeling, Identification and Control: A Norwegian Research Bulletin 27, no. 2 (2006): 95–108. http://dx.doi.org/10.4173/mic.2006.2.2.

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Lian, Kuang-Yow, Li-Sheng Wang, and Li-Chen Fu. "A skew-symmetric property of rigid-body systems." Systems & Control Letters 33, no. 3 (March 1998): 187–97. http://dx.doi.org/10.1016/s0167-6911(97)00110-2.

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Amer, T. S. "The Rotational Motion of the Electromagnetic Symmetric Rigid Body." Applied Mathematics & Information Sciences 10, no. 4 (July 1, 2016): 1453–64. http://dx.doi.org/10.18576/amis/100424.

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Lv, Wen Jun, and Xin Sheng Ge. "Energy-Based Inverted Equilibrium of the Axially Symmetric 3D Pendulum." Applied Mechanics and Materials 138-139 (November 2011): 128–33. http://dx.doi.org/10.4028/www.scientific.net/amm.138-139.128.

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In this paper, we study the attitude control problems based on model of the 3D axially symmetric rigid pendulum. Three degrees of freedom pendulum (3D pendulum) is a rigid body supported by a frictionless pivot. According to relative position of the center of mass and the fixed pivot without friction, the 3D rigid pendulum can be divided into two balanced attitudes, Hanging equilibrium and inverted equilibrium. When the 3D rigid pendulum in axis symmetric case, the axis of symmetry is equivalent to axis of inertia of rigid body, and angular velocity around the axis of symmetry is constant that not equal to zero, as a result, the 3D rigid pendulum equal to the axisymmetric rigid pendulum. According to the motion attitude of the axially symmetric 3D pendulum, this article proposes a control method based on passivity, By analyzing the dynamic characteristics, and demonstrate the dynamic characteristics to meet the passive condition. Firstly, we use the passivity theory, from total energy of the system, to research the equilibrium stability of the axially symmetric 3D pendulum in the inverted position. Secondly, to utilize the passivity theory and the Lyapunov function that we proposed to deduce the control law based on the energy method, so that the axially symmetric 3D pendulum to reach asymptotically stable in equilibrium position, and the simulation results verify the availability of the method.
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Cohen, H., and G. P. Mac Sithigh. "Symmetric and asymmetric roto-deformations of a symmetrical, isotropic, elastic pseudo-rigid body." International Journal of Non-Linear Mechanics 27, no. 4 (July 1992): 519–26. http://dx.doi.org/10.1016/0020-7462(92)90058-f.

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Tsiotras, P., and J. M. Longuski. "Analytic Solutions for a Spinning Rigid Body Subject to Time-Varying Body-Fixed Torques, Part II: Time-Varying Axial Torque." Journal of Applied Mechanics 60, no. 4 (December 1, 1993): 976–81. http://dx.doi.org/10.1115/1.2901011.

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In this paper we extend the methodology developed in Part I in order to accommodate the case of an axial time-varying torque (in addition to the two transverse timevarying torques) acting on a rotating rigid body. The analytic solutions thus derived describe the general attitude motion of a near-symmetric rigid body subject to timevarying torques about all three body-fixed axes.
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Atchonouglo, K., and K. Nwuitcha. "MATRIX STUDY OF THE EQUATION OF SOLID RIGID MOTIONS." Advances in Mathematics: Scientific Journal 10, no. 9 (September 13, 2021): 3195–207. http://dx.doi.org/10.37418/amsj.10.9.9.

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In this article, we described the equations of motion of a rigid solid by a matrix formulation. The matrices contained in our movement description are homogeneous to the same unit. Inertial characteristics are met in a 4x4 positive definite symmetric matrix called "tensor generalized Poinsot." This matrix consists of 3x3 positive definite symmetric matrix called "inertia tensor Poinsot", the coordinates of the center of mass multiplied by the total body mass and the total mass of the rigid body. The equations of motion are formulated as a gender skew 4x4 matrices. They summarize the "principle of fundamental dynamics". The Poinsot generalized tensor appears linearly in this equality as required by the linear dependence of the equations of motion with the ten characteristics inertia of the rigid solid.
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Maciejewski, Andrzej J. "Chaos and order in the Rotational Motion." International Astronomical Union Colloquium 132 (1993): 23–38. http://dx.doi.org/10.1017/s0252921100065891.

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AbstractIt was proved that the problem of perturbed planar oscillations of a rigid-body in a circular orbit is nonitegrable. Two types of perturbations were considered: solar radiations pressure and the third body torques. In the second part of the paper example of chaotic rotations of a symmetric rigid body in a circular orbit was given. It was shown numerically that the phase space is divided into two separate regions of chaotic and ordered motions.
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Bloch, Anthony M., Peter E. Crouch, Jerrold E. Marsden, and Tudor S. Ratiu. "The symmetric representation of the rigid body equations and their discretization." Nonlinearity 15, no. 4 (June 17, 2002): 1309–41. http://dx.doi.org/10.1088/0951-7715/15/4/316.

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Dissertations / Theses on the topic "Symmetric rigid body"

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De, Sousa Dias Maria Esmeralda Rodrigues. "Local dynamics of symmetric Hamiltonian systems with application to the affine rigid body." Thesis, University of Warwick, 1995. http://wrap.warwick.ac.uk/107563/.

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This work is divided into two parts. The first one is directed towards the geometric theory of symmetric Hamiltonian systems and the second studies the so-called affine rigid body under the setting of the first part. The geometric theory of symmetric Hamiltonian systems is based on Poisson and symplectic geometries. The symmetry leads to the conservation of certain quantities and to the reduction of these systems. We take special attention to the reduction at singular points of the momentum map. We survey the singular reduction procedures and we give a method of reducing a symmetric Hamiltonian system in a neighbourhood of a group orbit which is valid even when the momentum map is singular. This reduction process, which we called slice reduction, enables us to partially reduce the (local) dynamics to the dynamics of a system defined on a symplectic manifold which is the product of a symplectic vector space (symplectic slice) with a coadjoint orbit for the original symmetry group. The reduction represents the local dynamics as a coupling between vibrational motion on the vector space and generalized rigid body dynamics on the coadjoint group orbits. Some applications of the slice reduction are described, namely the application to the bifurcation of relative equilibria. We lay the foundations for the study of the affine rigid body under geometric methods. The symmetries of this problem and their relationship with the physical quantities are studied. The symmetry for this problem is the semi-direct product of the cyclic group of order two Z2 by 50(3) x 50(3). A result of Dedekind on the existence of adjoint ellipsoids of a given ellipsoid of equilibrium follows as consequence of the Z2 symmetry. The momentum map for the Z2 x, (50(3) x 50(3)) action on the phase space corresponds to the conservation of the angular momentum and circulation. Using purely geometric arguments Riemann’s theorem on the admissible equilibria ellipsoids for the affine rigid body is established. The symmetries of different relative equilibria are found, based on the study of the lattice of isotropy subgroups of Z2 x, (50(3) x 50(3)) on the phase space. Slice reduction is applied in a neighbourhood of a spherical ellipsoid of equilibrium leading to different reduced dynamics. Based also on the slice reduction we establish the bifurcation of S-type ellipsoids from a nondegenerate ellipsoidal equilibrium.
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Books on the topic "Symmetric rigid body"

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Maria Esmeralda Rodrigues de Sousa Dias. Local dynamics of symmetric Hamiltonian systems with application to the affine rigid body. [s.l.]: typescript, 1995.

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Book chapters on the topic "Symmetric rigid body"

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Dias, E. Sousa. "A Geometric Hamiltonian Approach to the Affine Rigid Body." In Dynamics, Bifurcation and Symmetry, 291–99. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0956-7_23.

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Modugno, M., C. Tejero Prieto, and R. Vitolo. "Geometric Aspects of the Quantization of a Rigid Body." In Differential Equations - Geometry, Symmetries and Integrability, 275–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00873-3_13.

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Parkin, I. A. "Linear Systems of Tan-Screws for Finite Displacement of a Rigid Body with Symmetries." In Advances in Robot Kinematics: Analysis and Control, 317–26. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-015-9064-8_32.

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Kotkin, Gleb L., and Valeriy G. Serbo. "Rigid-body motion. Non-inertial coordinate systems." In Exploring Classical Mechanics, 48–53. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198853787.003.0009.

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This chapter addresses the inertia tensor and its relation with the mass quadrupole moment tensor, the principal axes and the principal moments of inertia, evolution of the period of the Earth’s rotation around its axis due to the action of tidal forces, and the motion of the gyrocompass at a given latitude. The chapter also addresses precession of a symmetric top, the stability of rotations of an asymmetric top, “motion” of a plane disk which rolls in the field of gravity over a smooth horizontal plane, and the displacement from the vertical of a particle which is dropped from a given height with zero initial velocity. Finally, the chapter discusses the Lagrange point in the Sun-Jupiter system.
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Kotkin, Gleb L., and Valeriy G. Serbo. "Rigid-body motion. Non-inertial coordinate systems." In Exploring Classical Mechanics, 279–304. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198853787.003.0022.

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This chapter addresses the inertia tensor and its relation with the mass quadrupole moment tensor, the principal axes and the principal moments of inertia, evolution of the period of the Earth’s rotation around its axis due to the action of tidal forces, and the motion of the gyrocompass at a given latitude. The chapter also addresses precession of a symmetric top, the stability of rotations of an asymmetric top, “motion” of a plane disk which rolls in the field of gravity over a smooth horizontal plane, and the displacement from the vertical of a particle which is dropped from a given height with zero initial velocity. Finally, the chapter discusses the Lagrange point in the Sun-Jupiter system.
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Porter, Theodore M. "Time’s Arrow and Statistical Uncertainty in Physics and Philosophy." In The Rise of Statistical Thinking, 1820-1900, 204–41. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691208428.003.0008.

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This chapter explores how German economists and statisticians of the historical school viewed the idea of social or statistical law as the product of confusion between spirit and matter or, equivalently, between history and nature. That the laws of Newtonian mechanics are fully time-symmetric and hence can be equally run backwards or forwards could not easily be reconciled with the commonplace observation that heat always flows from warmer to cooler bodies. James Clerk Maxwell, responding to the apparent threat to the doctrine of free will posed by thermodynamics and statistics, pointed out that the second law of thermodynamics was only probable, and that heat could be made to flow from a cold body to a warm one by a being sufficiently quick and perceptive. Ludwig Boltzmann resisted this incursion of probabilism into physics but in the end he was obliged, largely as a result of difficulties presented by the issue of mechanical reversibility, to admit at least the theoretical possibility of chance effects in thermodynamics. Meanwhile, the American philosopher and physicist C. S. Pierce determined that progress—the production of heterogeneity and homogeneity—could never flow from rigid mechanical laws, but demanded the existence of objective chance throughout the universe.
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Ting, T. T. C. "Anisotropic Materials with an Elliptic Boundary." In Anisotropic Elasticity. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195074475.003.0013.

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The determination of stress distribution in a solid with the presence of a hole or an inclusion has been a mathematically interesting and challenging problem. It is also an important problem in applications. The simplest geometry of the hole is a circle. For isotropic materials a hole of arbitrary shape can be transformed, in theory, to a circle by a conformal mapping (Muskhelishvili, 1953; see also Section 3.12). Therefore a circular hole is all one needs to study for isotropic materials. For anisotropic materials there are three complex variables ɀα=x1+pαx2 (α=1,2,3). It is in general not possible to transform a hole of given shape to the same circle for all three complex variables. An exception is the ellipse (Lekhnitskii, 1950; Savin, 1961). In this chapter we study various problems involving an elliptic boundary. The ellipse can be a hole, a rigid body, or an inclusion of different anisotropic materials. We will also consider an elliptic body subjected to external forces. For anisotropic elastic materials even the circular hole needs a transformation. There is practically no difference in the analysis if the ellipse is replaced by a circle. We may employ dual coordinate systems. One coordinate system is chosen to coincide with a symmetry plane of the material when such a plane exists. The other coordinate system is to coincide with the principal axes of the ellipse. The analysis is no more complicated than when a single coordinate system is employed. For some problems employment of dual coordinate systems reveal that certain aspects of the solutions are invariant with the orientation of the ellipse in the material.
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Conference papers on the topic "Symmetric rigid body"

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Zheng, Qian, and Fen Wu. "Computationally Efficient Nonlinear H∞ Control Designs for a Rigid Body Spacecraft." In ASME 2008 Dynamic Systems and Control Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/dscc2008-2118.

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In this paper, we consider nonlinear control of a symmetric spacecraft about its axis of symmetry with two control torques. Using a computationally efficient ℋ∞ control design procedure, attitude regulation and trajectory tracking problems of the axi-symmetric spacecraft were solved. Resorting to higher order Lyapunov functions, the employed nonlinear ℋ∞ control approach reformulates the difficult Hamilton-Jacobian-Isaacs (HJI) inequalities as semi-definite optimization conditions. Sum-of-squares (SOS) programming techniques are then applied to obtain computationally tractable solutions, from which nonlinear control laws will be constructed. The proposed nonlinear ℋ∞ designs will be able to exploit the most suitable forms of Lyapunov function for spacecraft control and the resulting controllers will perform better than existing nonlinear control laws.
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DRAGOVIĆ, V., and B. GAJIĆ. "SKEW-SYMMETRIC LAX POLYNOMIAL MATRICES AND INTEGRABLE RIGID BODY SYSTEMS." In Perspectives of the Balkan Collaborations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702166_0019.

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Gupta, Krishna C. "Rigid Body Dynamical Equations With Lie Algebra." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/mech-14163.

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Abstract A direct derivation is presented for the Generalized Euler’s equation in the translated base system that is located at the center of mass of the body. The use of Lie algebra reveals an interesting property of the time-variant inertia matrix I(t) — its rate of change is the Lie product [Ω, I], where [Ω] is the skew-symmetric representation of the angular velocity ω. This observation also simplifies the derivation. The standard body system form and the ZRP-form are then deduced. With differing meanings of terms, all three forms have a similar appearance: MG = [I] α + [Ω] [I] ω.
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Beck, R., Mark Williams, and James Longuski. "Floquet solution for a spinning symmetric rigid body with constant transverse torques." In AIAA/AAS Astrodynamics Specialist Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1998. http://dx.doi.org/10.2514/6.1998-4385.

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Tsiotras, Panagiotis. "On the optimal regulation of an axi-symmetric rigid body with two controls." In Guidance, Navigation, and Control Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1996. http://dx.doi.org/10.2514/6.1996-3791.

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Kalpathy Venkiteswaran, Venkatasubramanian, Omer Anil Turkkan, and Hai-Jun Su. "Compliant Mechanism Design Through Topology Optimization Using Pseudo-Rigid-Body Models." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59946.

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The initial design of compliant mechanisms for a specific application can be a challenging task. This paper introduces a topology optimization approach for planar mechanisms based on graph theory. It utilizes pseudo-rigid-body models, which allow the kinetostatic equations to be represented as nonlinear algebraic equations. This reduces the complexity of the system compared to beam theory or finite element methods, and has the ability to incorporate large deformations. Integer variables are used for developing the adjacency matrix, which is optimized by a genetic algorithm. Dynamic penalty functions describe the general and case-specific constraints. A symmetric 3R model is used to represent the beams in the mechanism. The design space is divided into rectangular segments while kinematic and static equations are derived using kinematic loops. The effectiveness of the approach is demonstrated with the example of an inverter mechanism. The results are compared against finite element methods to prove the validity of the new model as well as the accuracy of the approach outlined here. Future implementations of this method will include stress and deformation analysis and also introduce multi-material designs using different pseudo-rigid-body models.
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Izadi, Maziar, Jan Bohn, Daero Lee, Amit K. Sanyal, Eric Butcher, and Daniel J. Scheeres. "A Nonlinear Observer Design for a Rigid Body in the Proximity of a Spherical Asteroid." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-4085.

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We consider an observer design for a spacecraft modeled as a rigid body in the proximity of an asteroid. The nonlinear observer is constructed on the nonlinear state space of motion of a rigid body, which is the tangent bundle of the Lie group of rigid body motions in three-dimensional Euclidean space. The framework of geometric mechanics is used for the observer design. States of motion of the spacecraft are estimated based on state measurements. In addition, the observer designed can also estimate the gravity parameter of the asteroid, assuming the asteroid to have a spherically symmetric mass distribution. Almost global convergence of state estimates and gravity parameter estimate to their corresponding true values is demonstrated analytically, and verified numerically.
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Fernandes, Antonio Carlos, Peyman Asgari, and Mohammadsharif Seddigh. "Roll Center of a FPSO in Regular Beam Seas for All Frequencies." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-41193.

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The so-called roll center is not a concept well defined for a rolling ship or platform when submitted to a wave field. The present paper discusses and proposes a clear definition. The paper shows a methodology to assess this point and shows that, for regular beam wave incidence on a symmetric body, the roll center is not necessarily located at the line of symmetry of the symmetric bodies. Also shows that the locus of the roll center is frequency dependent. Finally, the paper discusses the limits for low and high frequencies. This investigation uses basic equations of the rigid body kinematics and information for better understanding the complicated roll center. To validate the proposed methodology the paper reports model tests and frequency domain calculations regarding the behavior of the vessel in regular beam wave. A closed form equation for the calculation of the roll center is also proposed. All these results match very well. This is so, despite the very complicated phase behavior with frequency. The paper also addresses the question whether the bilge keels at each board should always be symmetric for a platform that will always operate in beams seas.
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Tasora, Alessandro, Dan Negrut, and Mihai Anitescu. "A GPU-Based Implementation of a Cone Convex Complementarity Approach for Simulating Rigid Body Dynamics With Frictional Contact." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66766.

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In the context of simulating the frictional contact dynamics of large systems of rigid bodies, this paper reviews a novel method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss-Seidel and Gauss-Jacobi methods with over-relaxation for symmetric convex linear complementarity problems. Convergent under fairly standard assumptions, the method is implemented in a parallel framework by using a single instruction multiple data computation paradigm promoted by the Compute Unified Device Architecture library for graphical processing unit programming. The framework supports the analysis of problems with a large number of rigid bodies in contact. Simulation thus becomes a viable tool for investigating the dynamics of complex systems such as ground vehicles running on sand, powder composites, and granular material flow.
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Ghosal, Ashitava, and Bahram Ravani. "A Dual Ellipse Is a Cylindroid." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5884.

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Abstract In this paper, we take a relook at two-degree-of-freedom instantaneous rigid body kinematics in terms of dual numbers and vectors, and show that a dual ellipse is a cylindroid. The instantaneous angular and linear velocities of a rigid body is expressed as a dual velocity vector, and the inner product of two dual vectors, as a dual number, is used. We show that the tip of a dual velocity vector lies on a dual ellipse, and the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of a positive definite, symmetric matrix whose elements are the dual numbers from the inner products. From the real and dual parts of the equation of the dual ellipse, we derive the equation of a cylindroid (Ball,1900).
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