Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 23 Oct 2019 18:47:49 GMT2019-10-23T18:47:49Z5071Corrigendum: Cubic polynomials on Lie groups: reduction of the Hamiltonian systemhttp://hdl.handle.net/10316/44963Title: Corrigendum: Cubic polynomials on Lie groups: reduction of the Hamiltonian system
Authors: Abrunheiro, Lígia; Camarinha, Margarida; Clemente-Gallardo, Jesús
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/449632013-01-01T00:00:00ZOptimal control of affine connection control systems from the point of view of Lie algebroidshttp://hdl.handle.net/10316/44964Title: Optimal control of affine connection control systems from the point of view of Lie algebroids
Authors: Abrunheiro, Lígia; Camarinha, Margarida
Abstract: The purpose of this paper is to use the framework of Lie algebroids to study
optimal control problems for affine connection control systems on Lie groups.
In this context, the equations for critical trajectories of the problem are
geometrically characterized as a Hamiltonian vector field.
Fri, 13 Jun 2014 00:00:00 GMThttp://hdl.handle.net/10316/449642014-06-13T00:00:00ZGeometric Hamiltonian Formulation of a Variational Problem Depending on the Covariant Accelerationhttp://hdl.handle.net/10316/44982Title: Geometric Hamiltonian Formulation of a Variational Problem Depending on the Covariant Acceleration
Authors: Abrunheiro, Lígia; Camarinha, Margarida; Clemente-Gallardo, Jesús
Abstract: In this work we consider a second order variational problem depending on the covariant acceleration, which is related with the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of the Pontryagin's maximum principle, allows us to study the dynamics of the control problem.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/449822013-01-01T00:00:00ZCubic polynomials and optimal control on compact Lie groupshttp://hdl.handle.net/10316/11187Title: Cubic polynomials and optimal control on compact Lie groups
Authors: Abrunheiro, L.; Camarinha, M.; Clemente-Gallardo, J.
Abstract: 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 canonical symplectic form on the cotangent bundle of the tangent bundle.
Using these control geometrical tools, the equivalence between the Hamiltonian
approach developed here and the known variational one is verified. Moreover, the
equivalence allows us to deduce two invariants along the cubic polynomials which
are in involution.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10316/111872009-01-01T00:00:00ZA second order Riemannian variational problem from a Hamiltonian perspectivehttp://hdl.handle.net/10316/11230Title: A second order Riemannian variational problem from a Hamiltonian perspective
Authors: Crouch, P.; Leite, F. Silva; Camarinha, M.
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*.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/10316/112301998-01-01T00:00:00ZOptimal control and quasi-velocitieshttp://hdl.handle.net/10316/13713Title: Optimal control and quasi-velocities
Authors: Abrunheiro, Lígia; Camarinha, Margarida; Cariñena, José F.; Clemente-Gallardo, Jesús; Martínez, Eduardo; Santos, Patricia
Abstract: In this paper we study optimal control problems for nonholonomic systems
defined on Lie algebroids by using quasi-velocities. We consider both kinemactic,
i.e. systems whose cost functional depends only on position and velocities, and
dynamic optimal control problems, i.e. systems whose cost functional depends also
on accelarations. Formulating the problem directly at the level of Lie algebroids
turns out to be the correct framework to explain in detail similar results appeared
recently [48]. We also provide several examples to illustrate our construction
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/137132010-01-01T00:00:00ZRiemannian cubic polynomialshttp://hdl.handle.net/10316/11423Title: Riemannian cubic polynomials
Authors: Abrunheiro, L.; Camarinha, M.
Abstract: 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 the system are obtained by means of invariants along the cubic
polynomials.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10316/114232004-01-01T00:00:00Z