Geometric Integration of Non-autonomous Systems with Application to Rotor Dynamics

TL;DR

This paper demonstrates that geometric (structure-preserving) integration algorithms outperform traditional methods in simulating non-autonomous systems like rotor dynamics, through numerical experiments and backward error analysis.

Contribution

It introduces the application of geometric integration techniques to non-autonomous systems, highlighting their advantages over conventional methods in engineering problems.

Findings

Geometric integrators show superior accuracy in rotor dynamics simulations.

Backward error analysis confirms the stability of geometric methods.

Numerical results validate the theoretical advantages of structure-preserving algorithms.

Abstract

Geometric integration of non-autonomous classical engineering problems, such as rotor dynamics, is investigated. It is shown, both numerically and by backward error analysis, that geometric (structure preserving) integration algorithms are superior to conventional Runge-Kutta methods.