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Discrete variational Lie group formulation of geometrically exact beam dynamics

Abstract : The goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics, by using a Lie group variational integrator. Both spatial and temporal discretization are implemented in a geometry preserving manner. The resulting scheme preserves both the discrete momentum maps and symplectic structures, and exhibits almost-perfect energy conservation. Comparisons with existing numerical schemes are provided and the convergence behavior is analyzed numerically.
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https://hal.archives-ouvertes.fr/hal-01396186
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Submitted on : Monday, November 14, 2016 - 10:37:56 AM
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F. Demoures, F. Gay-Balmaz, S. Leyendecker, S. Ober-Blöbaum, T. S. Ratiu, et al.. Discrete variational Lie group formulation of geometrically exact beam dynamics. Numerische Mathematik, Springer Verlag, 2015, 130 (1), pp.73-123. ⟨10.1007/s00211-014-0659-4⟩. ⟨hal-01396186⟩

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