Hamilton-Pontryagin Integrators on Lie Groups: Introduction and Structure-Preserving Properties - Mathematics > Numerical AnalysisReport as inadecuate




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Abstract: In this paper structure-preserving time-integrators for rigid body-typemechanical systems are derived from a discrete Hamilton-Pontryagin variationalprinciple. From this principle one can derive a novel class of variationalpartitioned Runge-Kutta methods on Lie groups. Included among these integratorsare generalizations of symplectic Euler and St\-{o}rmer-Verlet integrators fromflat spaces to Lie groups. Because of their variational design, theseintegrators preserve a discrete momentum map in the presence of symmetry anda symplectic form.In a companion paper, we perform a numerical analysis of these methods andreport on numerical experiments on the rigid body and chaotic dynamics of anunderwater vehicle. The numerics reveal that these variational integratorspossess structure-preserving properties that methods designed to preservemomentum using the coadjoint action of the Lie group and energy for example,by projection lack.



Author: Nawaf Bou-Rabee, Jerrold E. Marsden

Source: https://arxiv.org/







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