Symplectic, linearly-implicit and stable integrators, with applications to constrained dynamics

Details Symplectic, linearly-implicit and stable integrators, with applications to constrained dynamics Symplectic, linearly-implicit and stable integrators, with applications to constrained dynamics

2011-03-23

arxiv.org/abs/1103.4645v2

Mathematics

Numerical Analysis

Scientific paper

We introduce a family of symplectic, linearly-implicit and stable integrators for mechanical systems. When used in conjunction with penalty methods (i.e., methods that consist in replacing constraints by stiff potentials), these integrators accelerate the numerical simulation of mechanical systems with holonomic constraints by employing coarse timesteps and bypassing the resolution of nonlinear systems. Although penalty methods are well known and widely employed, a general and rigorous proof of their accuracy appeared to be lacking; such a proof is also provided in this paper.

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