Splitting methods for Levitron Problems
For researchers simulating magnetostatic traps, this work offers more accurate and efficient numerical schemes, though it is an incremental improvement on existing splitting methods.
The paper proposes novel splitting methods for simulating Levitron systems, achieving improved accuracy over the Verlet integrator through iterative and extrapolation techniques, while saving computational time.
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.