Solving Linearized Equations of the N-body Problem Using the Lie-integration Method
نویسنده
چکیده
Several integration schemes exits to solve the equations of motion of the N -body problem. The Lie-integration method is based on the idea to solve ordinary differential equations with Lie-series. In the 1980s this method was applied for the N -body problem by giving the recurrence formula for the calculation of the Lie-terms. The aim of this works is to present the recurrence formulae for the linearized equations of motion of N -body systems. We prove a lemma which greatly simplifies the derivation of the recurrence formulae for the linearized equations if the recurrence formulae for the equations of motions are known. The Lie-integrator is compared with other well-known methods. The optimal step size and order of the Lie-integrator are calculated. It is shown that a fine-tuned Lie-integrator can be 30%-40% faster than other integration methods.
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