Please use this identifier to cite or link to this item:
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 |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
A second order Riemannian variational problem from a Hamiltonian perspective.pdf | 205.52 kB | Adobe PDF | View/Open |
Page view(s)
259
checked on Sep 24, 2024
Download(s)
99
checked on Sep 24, 2024
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.