论文信息 - A symplectic integrator for riemannian manifolds

A symplectic integrator for riemannian manifolds

SummaryThe 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.

Benedict Leimkuhler | George W. Patrick

[1] P J Fox,et al. THE FOUNDATIONS OF MECHANICS. , 1918, Science.

[2] Sebastian Reich,et al. Symplectic Integrators for Systems of Rigid Bodies , 1996 .

[3] P. Crouch,et al. Numerical integration of ordinary differential equations on manifolds , 1993 .

[4] H. Yoshida. Construction of higher order symplectic integrators , 1990 .

[5] R. McLachlan,et al. Equivariant constrained symplectic integration , 1995 .

[6] J. Marsden. Lectures on Mechanics , 1992 .

[7] I. Holopainen. Riemannian Geometry , 1927, Nature.

[8] Benedict Leimkuhler,et al. Symplectic Methods For Conservative Multibody Systems , 1993 .

[9] J. C. Simo,et al. Conserving algorithms for the dynamics of Hamiltonian systems on lie groups , 1994 .

[10] J. Marsden,et al. Introduction to mechanics and symmetry , 1994 .

[11] B. Leimkuhler,et al. Symplectic integration of constrained Hamiltonian systems , 1994 .

[12] H. Munthe-Kaas. Lie-Butcher theory for Runge-Kutta methods , 1995 .

[13] J. C. Simo,et al. Conserving algorithms for the n dimensional rigid body , 1995 .

[14] J. Marsden. Two Axially Symmetric Coupled Rigid Bodies: Relative Equilibria, Stability, Bifurcations, and a Momentum Preserving Symplectic Integrator , 1991 .