Foundations of Computational Mathematics

, Volume 17, Issue 1, pp 199–257 | Cite as

Lie Group Spectral Variational Integrators

  • James Hall
  • Melvin Leok


We present a new class of high-order variational integrators on Lie groups. We show that these integrators are symplectic and momentum-preserving, can be constructed to be of arbitrarily high order, or can be made to converge geometrically. Furthermore, these methods are capable of taking very large time-steps. We demonstrate the construction of one such variational integrator for the rigid body and discuss how this construction could be generalized to other related Lie group problems. We close with several numerical examples which demonstrate our claims and discuss further extensions of our work.


Symplectic integrators Variational integrators Lie group integrators Geometric numerical integration 

Mathematics Subject Classification

37M15 65M70 65P10 70G75 70H25 



This work was supported in part by NSF Grants CMMI-1029445, DMS-1065972, CMMI-1334759, DMS-1411792, DMS-1345013, and NSF CAREER Award DMS-1010687.


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Copyright information

© SFoCM 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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