Astronomy and Astrophysics – Astrophysics
Scientific paper
1999-06-19
Astron.J.118:2532-2541,1999
Astronomy and Astrophysics
Astrophysics
24 pages, 3 figures, submitted to Astronomical Journal; minor errors in equations and one figure corrected
Scientific paper
10.1086/301102
Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive timestep control is added to a symplectic integrator. We describe an adaptive-timestep symplectic integrator that can be used if the Hamiltonian is the sum of kinetic and potential energy components and the required timestep depends only on the potential energy (e.g. test-particle integrations in fixed potentials). In particular, we describe an explicit, reversible, symplectic, leapfrog integrator for a test particle in a near-Keplerian potential; this integrator has timestep proportional to distance from the attracting mass and has the remarkable property of integrating orbits in an inverse-square force field with only "along-track" errors; i.e. the phase-space shape of a Keplerian orbit is reproduced exactly, but the orbital period is in error by O(1/N^2), where N is the number of steps per period.
Preto Miguel
Tremaine Scott
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