Journal of Nonlinear Science

, Volume 6, Issue 4, pp 367–384 | Cite as

A symplectic integrator for riemannian manifolds

  • B. Leimkuhler
  • G. W. Patrick


The configuration spaces of mechanical systems usually support Riemannian metrics which have explicitly solvable geodesic flows and parallel transport operators. While not of primary interest, such metrics can be used to generate integration algorithms by using the known parallel transport to evolve points in velocity phase space.


Riemannian Manifold Symmetric Space Configuration Space Riemannian Geometry Exponential Mapping 
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Copyright information

© Springer-Verlag New York Inc. 1996

Authors and Affiliations

  • B. Leimkuhler
    • 1
  • G. W. Patrick
    • 2
  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA
  2. 2.Department of Mathematics and StatisticsUniversity of SaskatchewanSaskatoonCanada

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