A symmetric splitting method for rigid body dynamics

A symmetric splitting method for rigid body dynamics

It has been known since the time of Jacobi that the solution to the free rigid body (FRB) equations of motion is given in terms of a certain type of elliptic functions. Using the Arithmetic-Geometric mean algorithm, [1], these functions can be calculated efficiently and accurately. The overall approach yields a faster and more accurate numerical solution to the FRB equations compared to standar...

Recursive Taylor Series Expansion Method for Rigid-Body Molecular Dynamics.

Molecular dynamics computer simulation methods are very important for understanding mechanisms of chemical, physical, and biological processes. The reliability of molecular dynamics simulations strongly depends on the integration schemes used in the simulations. In this work, we developed new rigid body integration schemes for molecular dynamics simulations. Our approach is based on a numerical...

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...