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Variational integrators are momentum-preserving and symplectic numericalmethods used to propagate the evolution of Hamiltonian systems. In this paper,we introduce a new class of variational integrators that achieve fourth-orderconvergence despite having the same integration scheme as traditionalsecond-order variational integrators. The new class of integrators are createdby replacing a dynamical system's Lagrangian in the variational integrationalgorithm with its surrogate Lagrangian. By incorporating the surrogateLagrangian the propagation errors induced by variational integrators, up to agiven order, are eliminated. Furthermore, no assumption on the Lagrangian'sstructure is made and, therefore, the proposed approach is applicable to alarge range of dynamical systems. In addition, surrogate variationalintegrators are also constructed for Hamiltonian systems subjected to holonomicconstraints and external forces. Finally, the methodology is extended to derivehigher-order surrogate variational integrators that achieve an arbitrary orderof accuracy but retain second-order complexity in the integration scheme.Several numerical experiments are presented to demonstrate the efficacy of ourapproach.

Surrogate Lagrangians for Variational Integrators: High Order Convergence with Low Order Schemes