Variational Integrators for Stochastic Mechanical Hybrid Systems

This paper introduces stochastic variational impact integrators for the class of hybrid mechanical systems that incorporate random noise. The governing equations are obtained by the application of the variational principle to the stochastic action integral, where both the continuous-time dynamics as well as the discrete transitions are considered. Furthermore, structure-preserving geometric integrators are derived through the discretization of the stochastic variational principle. This ensures the consistency in comparison to the continuous versions of the Euler-Lagrange or Hamilton’s equations. The effectiveness of the proposed methods in capturing the long-term energy behavior of a stochastic mechanical hybrid system is illustrated by numerical examples.