Statistics – Computation
Scientific paper
Jul 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002jnuns..38..462w&link_type=abstract
Journal of Nanjing University (Natural Sciences) [Nanjing Daxue Xuebao (Ziran Kexue)] (ISSN 0469-5097), Vol. 38, No. 4, p. 462 -
Statistics
Computation
Solar System Dynamics, Numerical Methods, Symplectic Methods
Scientific paper
Symplectic methods are so far the best numerical methods for qualitative exploration in solar system dynamics. They maintain the symplectic structure and key properties of Hamiltonian systems and do not bring in any artificial dissipation, making possible long-term numerical integrations with a large step size. The symplectic method that has been widely adopted in references on qualitative studies of solar system dynamics is the method worked out by Wisdom and Holman (SYA). It is built in the Jacobian coordinate system and takes an approximation of the Hamiltonian. The Wisdom and Holman's method for an exact Hamiltonian is abbreviated as SYP. Actually a symplectic integrator can be built in the barycentric coordinate system (SYS), which separates the Hamiltonian into two parts, the potential energy and the kinetic energy. Here we propose a quasi-symplectic method SYQ in the barycentric coordinate system. An extensive comparative study of these four types of methods is given, especially on their computation efficiency and error accumulation. This research draws the following conclusion. Considering that symplectic integrators are mainly used in exploring the qualitative evolution of dynamical systems and a high precision is not required, SYS should not be recommended in solar system dynamics for its low efficiency. During a 108 years integration, SYP methods cause almost the same errors on the positions of the planets but they take about 40% more computing time. We thus believe that SYP cannot compete with SYA or SYQ, but it is hard to tell SYA or SYQ is better. Our research has also shown that resonances play a role in keeping the orbit configuration of a planetary system during long-term numerical integrations.
Huang Tianyi
Wan Xiaosheng
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