Affine body dynamics

Dynamics of Linear and Affine Maps

The well-known theory of the “rational canonical form of an operator” describes the invariant factors, or equivalently, elementary divisors, as a complete set of invariants of a similarity class of an operator on a finite-dimensional vector space V over a given field F. A finer part of the theory is the contribution by Frobenius dealing with the structure of the centralizer of an operator. The ...

Audio to Body Dynamics

We present a method that gets as input an audio of violin or piano playing, and outputs a video of skeleton predictions which are further used to animate an avatar. The key idea is to create an animation of an avatar that moves their hands similarly to how a pianist or violinist would do, just from audio. Aiming for a fully detailed correct arms and fingers motion is a goal, however, it’s not c...

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...