Reducing round-off errors in rigid body dynamics

Reducing round-off errors in rigid body dynamics

In several recent publications, numerical integrators based on Jacobi elliptic functions are proposed for solving the equations of motion of the rigid body. Although this approach yields theoretically the exact solution, a standard implementation shows an unexpected linear propagation of round-off errors. We explain how deterministic error contribution can be avoided, so that round-off behaves ...

Reducing round-off errors in symmetric multistep methods

Certain symmetric linear multistep methods have an excellent long-time behavior when applied to second order Hamiltonian systems with or without constraints. For high accuracy computations round-off can be the dominating source of errors. This article shows how symmetric multistep methods should be implemented, so that round-off errors are minimized and propagate like a random walk.

Off-line Model Simplification for Interactive Rigid Body Dynamics Simulations

Rigid body dynamics simulations require use of accurate computation of contacts among bodies. Often collision detection algorithms are used for determining the contact between moving bodies. Mechanical parts have a large number of features and hence collision detection with the detailed part models often slows down the rigid body dynamics simulations. In many simulation scenarios, all the parts...

Periodicity and Transport from Round-Off Errors

AMS Subject Classi cation: 58F20, 60J60, 65G05 We investigate the effects of round-off errors on quasi-periodic motions in a linear symplectic planar map. By discretizing coordinates uniformly we transform this map into a permutation of Z2 , and study motions near infinity, which correspond to a fine discretization. We provide numerical evidence that all orbits are periodic and that the average...

Title : Rigid body dynamics