Integration of Hamiltonian systems with a structure preserving algorithm
Paper in proceedings, 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.

structure preserving integrators

chaos

Runge-Kutta

Hamiltonian

leap-frog

spring-pendulum

Author

Sadegh Rahrovani

Dynamics

Thomas Abrahamsson

Dynamics

Klas Modin

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

26th International Conference on Noise and Vibration Engineering, ISMA 2014, Including the 5th International Conference on Uncertainty in Structural Dynamics, USD 2014; Leuven; Belgium; 15 September 2014 through 17 September 2014

2915-2929

Subject Categories

Mechanical Engineering

Computational Mathematics

Areas of Advance

Materials Science

ISBN

978-90-73-80291-9

More information

Created

10/7/2017