Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1896094 | Physica D: Nonlinear Phenomena | 2012 | 11 Pages |
The goal of this paper is to show that the space–time geodesic approach of classical mechanics can be used to generate a time adaptive variational integration scheme. The only assumption we make is that the Lagrangian for the system is in a separable form. The geometric structure which is preserved in the integration scheme is made explicit and the algorithm is illustrated with simulation for a compact case, a non-compact case, a chaotic system which arises as a perturbation of an integrable system and the figure eight solution for a three body problem.
► We show that standard Euler–Lagrange equations are equivalent to geodesic equations.► The geodesic formulation enables time adaptive variational integrator for the dynamics.► We demonstrate precisely in what sense the scheme is symplectic.► We conclude with simulation results for integrable, chaotic and high dimensional three body example.