On Cartesian stiffness matrices in rigid body dynamics: an energetic perspective

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...

The rigid body dynamics on SO ( 4 )

It is shown that for the generalized rigid body certain Cartan subalgebras (called of coordinate type) of so(n) are equilibrium points for the rigid body dynamics. In the case of so(4) there are three coordinate type Cartan subalgebras which form the set of all the regular equilibria. These coordinate type Cartan subalgebras are the analogues of the three axes of equilibria for the classical ri...

On Flexible Body Approximations of Rigid Body Dynamics

This paper demonstrates that techniques in flexible body dynamics can yield surprising results when applied to rigid bodies. The discussion presents a technique for constructing rigid bodies from collections of masses and springs, and demonstrates that the simulation calculates many features of rigid body dynamics such as the behavior of the center of mass and the moments of inertia, free of ch...