Integration of Hamiltonian systems with a structure preserving algorithm

Paper in proceeding, 2014

The disability of classical general-purpose integrators, such as the Runge-Kutta integrators, to exploit/preserve the structure of the analytical system and the failure of traditional structure-preserving geometric integrators, such as the leapfrog method, in treating highly oscillatory problems has been the main motivation for development of a recently proposed symplectic exponential integrator. Here, the capability of the method in robust simulation of Hamiltonian systems with complex dynamical behaviour, such as the elastic pendulum benchmark, is studied. The method exactly conserves the motion invariants, such as the angular momentum, while approximately conserves the Hamiltonian function. Furthermore, the method performance has been validated for systems with highly oscillatory behavior. These advantages are of particular interest for a variety of problems encountered in mechanical engineering applications, such as simulation of spacecraft structures, rotor blades, and similar systems.