Rigid Body Dynamics Using Clifford Algebra

On using computer algebra systems for analysis of rigid body dynamics

Usage of modern computer algebra (CA) tools allows one to extend significantly number of effective algorithms for qualitative investigation of dynamic systems. This report discusses some of the algorithms which generalize the Rauth-Lyapunov method of analysis of conservative systems with several first algebraic integrals: 1. Using enveloping integral of family of first integrals for finding inv...

Rigid-Body Pose and Position Interpolation using Geometric Algebra

This paper presents a method of interpolating between two or more general displacements (rotation and translation). The resulting interpolated path is smooth and possesses a number of desirable properties. It differs from existing algorithms which require factorising the pose into separate rotation and translation components and is derived from an intuitively appealing framework – i.e. a natura...

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...