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https://hdl.handle.net/10316/11230
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*. | URI: | https://hdl.handle.net/10316/11230 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Vários |
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A second order Riemannian variational problem from a Hamiltonian perspective.pdf | 205.52 kB | Adobe PDF | View/Open |
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