Symplectic Numerical Methods and Some Practical Aspects of their Application for Engineering Problems

Abstract

The use of various numerical simulations proves to be indispensable in contemporary mechanical engineering. The present work investigates a special type of the numerical methods used for simulating dynamical systems, the symplectic schemes, which belong to the broader class of structure-preserving numerical methods. We apply the symplectic schemes to a nonlinear dynamic system, the mechanical model of a planar elastic pendulum, and using our results we contrast them with a few widely used classical methods. Compared to these, the symplectic methods give more accurate results in both the quantitative and qualitative sense, with the same or even lower computational demand. We also discuss the limitations and specifics of their practical applications, some of their possible extensions, and show that the accuracy of the numerical results depends on the chosen coordinate system.