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DISCRETE SECOND-ORDER EULER–POINCARÉ EQUATIONS: APPLICATIONS TO OPTIMAL CONTROL

LEONARDO COLOMBO

Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Calle Nicolás Cabrera 15, 28049 Madrid, Spain

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FERNANDO JIMÉNEZ

Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Calle Nicolás Cabrera 15, 28049 Madrid, Spain

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DAVID MARTÍN DE DIEGO

Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Calle Nicolás Cabrera 15, 28049 Madrid, Spain

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https://doi.org/10.1142/S0219887812500375Cited by:9 (Source: Crossref)

Abstract

In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on Lie groups, deriving a discrete version of the second-order Euler–Lagrange equations. Interesting applications as, for instance, a discrete derivation of the Euler–Poincaré equations for second-order Lagrangians and its application to optimal control of a rigid body, and of a Cosserat rod are shown at the end of the paper.

Keywords:

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