A symplectic integrator for riemannian manifolds
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.
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- R. Abraham and J. E. Marsden,Foundationsof Mechanics. Addision-Wesley, Reading, MA, second edition, 1978.Google Scholar
- E. Barth and B. Leimkuhler. Symplectic methods for conservative multibody systems.Fields Inst. Commun., 1995. To appear.Google Scholar
- W. M. Boothby.An Introduction to Riemannian Geometry. Academic Press, New York, 1975.Google Scholar
- W. Klingenberg.Riemannian Geometry. Walter de Gruyter, New York, 1982Google Scholar
- D. Lewis and J. C. Simo. Conserving algorithms for then dimensional rigid body.Fields Inst. Commun., 1995. To appear.Google Scholar
- J. E. Marsden,Lectures on Mechanics, volume 174 ofLondon Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1992.Google Scholar
- J. E. Marsden and T. S. Ratiu.Introduction to Mechanics and Symmetry. Springer-Verlag, New York, 1994.Google Scholar
- H. Munthe-Kaas. Lie-Butcher theory for Runge-Kutta methods.BIT, 35, 1995.Google Scholar
- G. W. Patrick.Two axially symmetric coupled rigid bodies: Relative equilibria, stability, bifurcations, and a momentum preserving, symplectic integrator. Ph.D. thesis, University of California at Berkeley, 1991.Google Scholar
- S. Reich. Symplectic integrators for systems of rigid bodies.Fields Inst. Commun., 1995. to appear.Google Scholar