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Cubic polynomials and optimal control on compact Lie groups
Abrunheiro, L.; Camarinha, M.; Clemente-Gallardo, J.This paper analyzes the Riemannian cubic polynomials’s problem from a Hamiltonian point of view. The description of the problem on compact Lie groups is particulary explored. The state space of the second order optimal control problem considered is the tangent bundle of the Lie group which also has a group structure. The dynamics of the problem is described by a presymplectic formalism associated with the canon...
Riemannian cubic polynomials
Abrunheiro, L.; Camarinha, M.This paper gives an analysis of the Riemannian cubic polynomials, with special interest in the Lie group SO(3), based on the study of a second order variational problem. The corresponding Euler-Lagrange equation gives rise to an interesting system of nonlinear di erential equations. Motivated by the problem of the motion of a rigid body, the reduction of the essential size and the separation of the variables of...
A second order Riemannian variational problem from a Hamiltonian perspective
Crouch, P.; Leite, F. Silva; Camarinha, M.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...
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