Splitting methods for Levitron Problems

Details Splitting methods for Levitron Problems Splitting methods for Levitron Problems

2012-01-09

arxiv.org/abs/1201.1736v1

Physics

Mathematical Physics

17 pages

Scientific paper

In this paper we describe splitting methods for solving Levitron, which is motivated to simulate magnetostatic traps of neutral atoms or ion traps. The idea is to levitate a magnetic spinning top in the air repelled by a base magnet. The main problem is the stability of the reduced Hamiltonian, while it is not defined at the relative equilibrium. Here it is important to derive stable numerical schemes with high accuracy. For the numerical studies, we propose novel splitting schemes and analyze their behavior. We deal with a Verlet integrator and improve its accuracy with iterative and extrapolation ideas. Such a Hamiltonian splitting method, can be seen as geometric integrator and saves computational time while decoupling the full equation system. Experiments based on the Levitron model are discussed.

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