2010/06/30 by Ch. Skokos, E. Gerlach · 2 citations
Physics and Astronomy · Mathematics · #nlin.CD #astro-ph.EP #astro-ph.GA #math-ph #math.MP #physics.comp-ph
paper · pdf · doi:10.1103/physreve.82.036704
published as Phys.Rev.E82:036704,2010 · 27 pages, 11 figures, to appear in Phys. Rev. E
arxiv created 2010/09/29 · arxiv updated 2015/03/16
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom, and investigate their efficiency in accurately reproducing well-known properties of chaos indicators like the Lyapunov Characteristic Exponents (LCEs) and the Generalized Alignment Indices (GALIs). We find that the best numerical performance is exhibited by the `tangent map (TM) method', a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy. According to this method, a symplectic integrator is used to approximate the solution of the Hamilton's equations of motion by the repeated action of a symplectic map S, while the corresponding tangent map TS, is used for the integration of the variational equations. A simple and systematic technique to construct TS is also presented.