The free rigid body dynamics: Generalized versus classic

Title : Rigid body dynamics

3D Rigid Body Dynamics

The difficulty of describing the positions of the body-fixed axis of a rotating body is approached through the use of Euler angles: spin ψ̇, nutation θ and precession φ shown below in Figure 1. In this case we surmount the difficulty of keeping track of the principal axes fixed to the body by making their orientation the unknowns in our equations of motion; then the angular velocities and angula...

Frictional Rigid Body Dynamics

Practical problems like regulating robot grippers critically rely on accurately predicted friction forces. Qualified methods are derived and discussed subsequently. Special attention is paid to the question of solution existence. A time-stepping scheme which supports Coulomb friction and inelastic impacts is implemented and the numerical results are analyzed. The approach proofs to be stable, a...

Relative Equilibria for the Generalized Rigid Body

This paper gives necessary and sufficient conditions for the (n-dimensional) generalized free rigid body to be in a state of relative equilibrium. The conditions generalize those for the case of the three-dimensional free rigid body, namely that the body is in relative equilibrium if and only if its angular velocity and angular momentum align, that is, if the body rotates about one of its princ...

GPU-Based Rigid Body Dynamics

The simulation of rigid body dynamics is an area of interest both for scientific research and engineering applications. The accurate numerical solution of the underlying complementarity problems is complex. The use of the computational power of current graphics processing units (GPUs) to solve these systems seems promising. Using NVIDIA ’s CUDA technology for General-Purpose computation on Grap...