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On the geometry of higher-order variational problems on Lie groups (1104.3221v1)
Published 16 Apr 2011 in math-ph, cs.SY, math.DG, math.MP, and math.OC
Abstract: In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting applications as, for instance, a geometric derivation of the higher-order Euler-Poincar\'e equations, optimal control of underactuated control systems whose configuration space is a Lie group are shown, among others, along the paper.