Reduction of a Gyrostat Problem to That of a Rigid Body

1973 ◽  
Vol 40 (1) ◽  
pp. 105-108
Author(s):  
T. R. Kane ◽  
B. S. Chia
Keyword(s):  
Rigid Body ◽  
Body Problem ◽  
Dynamical Equations ◽  
Rotational Motions

To determine the motion of a symmetric gyrostat under the action of a specialized body-fixed force, dynamical equations governing rotational motions are solved, and it is then shown how results available from a certain rigid-body problem can be used to complete the integration of the remaining kinematical and dynamical equations.

Nature of the Requirements for Reference Coordinate Systems

1975 ◽  
Vol 26 ◽  
pp. 49-62
Author(s):  
C. A. Lundquist
Keyword(s):  
Rigid Body ◽  
Coordinate System ◽  
Equations Of Motion ◽  
Inertial Reference Frame ◽  
Earth System ◽  
Coordinate Systems ◽  
Dynamical Equations ◽  
The Earth ◽  
Measurement Uncertainties ◽  
Rotational Motions

AbstractThe current need for more precisely defined reference coordinate systems arises for geodynamics because the Earth can certainly not be treated as a rigid body when measurement uncertainties reach the few centimeter scale or its angular equivalent. At least two coordinate systems seem to be required. The first is a system defined in space relative to appropriate astronomical objects. This system should approximate an inertial reference frame, or be accurately related to such a reference, because only such a coordinate system is suitable for ultimately expressing the dynamical equations of motion for the Earth. The second required coordinate system must be associated with the nonrigid Earth in some well defined way so that the rotational motions of the whole Earth are meaningfully represented by the transformation parameters relating the Earth system to the space-inertial system. The Earth system should be defined so that the dynamical equations for relative motions of the various internal mechanical components of the Earth and accurate measurements of these motions are conveniently expressed in this system.

Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics

2007 ◽  
Author(s):  
Sigrid Leyendecker ◽  
Sina Ober-Blo¨baum ◽  
Jerrold E. Marsden ◽  
Michael Ortiz
Keyword(s):  
Optimal Control ◽  
Rigid Body ◽  
Null Space ◽  
Numerical Dissipation ◽  
Discrete Version ◽  
Dynamical Equations ◽  
Time Stepping ◽  
Minimal Dimension ◽  
Energy And Momentum ◽  
External Forces

This paper formulates the dynamical equations of mechanics subject to holonomic constraints in terms of the states and controls using a constrained version of the Lagrange-d’Alembert principle. Based on a discrete version of this principle, a structure preserving time-stepping scheme is derived. It is shown that this respect for the mechanical structure (such as a reliable computation of the energy and momentum budget, without numerical dissipation) is retained when the system is reduced to its minimal dimension by the discrete null space method. Together with initial and final conditions on the configuration and conjugate momentum, the reduced time-stepping equations serve as nonlinear equality constraints for the minimisation of a given cost functional. The algorithm yields a sequence of discrete configurations together with a sequence of actuating forces, optimally guiding the system from the initial to the desired final state. The resulting discrete optimal control algorithm is shown to have excellent energy and momentum properties, which are illustrated by two specific examples, namely reorientation and repositioning of a rigid body subject to external forces and the reorientation of a rigid body with internal momentum wheels.

Displacement of the Lagrange Equilibrium Points in the Restricted Three Body Problem With Rigid Body Satellite

1978 ◽  
Vol 41 ◽  
pp. 305-314
Author(s):  
W.J. Robinson
Keyword(s):  
Rigid Body ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

AbstractIn the restricted problem of three point masses, the positions of the equilibrium points are well known and are tabulated. When the satellite is a rigid body, these values no longer correspond to the equilibrium points. This paper seeks to determine the magnitudes of the discrepancies.

scholarly journals Pulsating curves of zero velocity for infinitesimal mass around oblate and triaxial rigid body of triangular equilibrium points in elliptical restricted three body problem

2017 ◽  
Vol 5 (1) ◽  
pp. 29
Author(s):  
Nutan Singh ◽  
A. Narayan
Keyword(s):  
Rigid Body ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Triaxial Rigid Body ◽  
Three Body ◽  
Infinitesimal Mass

This paper explore pulsating Curves of zero velocityof the infinitesimal mass around the triangular equilibrium points with oblate and triaxial rigid body in the elliptical restricted three body problem(ER3BP).

Nonlinear Hall MHD and electrostatic ion–cyclotron stationary waves: a Hamiltonian-geometric viewpoint

2007 ◽  
Vol 73 (5) ◽  
pp. 687-700 ◽  
Author(s):  
J. F. McKENZIE ◽  
R. L. MACE ◽  
T. B. DOYLE
Keyword(s):  
Rigid Body ◽  
Periodic Solutions ◽  
Soliton Solutions ◽  
Stationary Waves ◽  
Dynamical Equations ◽  
Free Rigid Body ◽  
Ion Cyclotron ◽  
Hall Mhd

AbstractSome supplementary results and interpretations on the theory of Hall MHD solitons (McKenzie and Doyle 2002 Phys. Plasmas9, 55) are presented. It is shown that the Hall MHD soliton reduces, in the appropriate limit, to an electrostatic ion–cyclotron soliton. It is also shown how the dynamical equations governing the Hall MHD soliton can be obtained from a Hamiltonian H. Soliton solutions correspond to H = 0, periodic solutions to H < 0 and rotation-type solutions to H >0. Possible applications are discussed. A non-canonical Hamiltonian picture is developed and compared to the well-known example of a free rigid body.

scholarly journals Rigid Body Trajectories in Different 6D Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Carol Linton ◽  
William Holderbaum ◽  
James Biggs
Keyword(s):  
Euclidean Space ◽  
Rigid Body ◽  
Hyperbolic Space ◽  
Poisson Structure ◽  
Scaling Factor ◽  
The Body ◽  
Body Frame ◽  
Spatial Frame ◽  
Axis Of Symmetry ◽  
Rotational Motions

The objective of this paper is to show that the group with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.

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