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Title: A second order Riemannian variational problem from a Hamiltonian perspective
Authors: Crouch, P. 
Leite, F. Silva 
Camarinha, M. 
Keywords: Riemannian manifolds; Lie groups; Hamiltonian equations; Optimal control; Variational problems
Issue Date: 1998
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 98-17 (1998)
Abstract: We present a Hamiltonian formulation of a second order variational problem on a differentiable manifold Q, endowed with a Riemannian metric < .,.> and explore the possibility of writing down the extremal solutions of that problem as a flow in the space TQ T*Q T*Q. For that we utilize the connection r on Q, corresponding to the metric < .,.>. In general the results depend upon a choice of frame for TQ, but for the special situation when Q is a Lie group G with Lie algebra G, our results are global and the flow reduces to a flow on G x G x G* x G*.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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