3,687 research outputs found
Variational integrators and time-dependent lagrangian systems
This paper presents a method to construct variational integrators for
time-dependent lagrangian systems. The resulting algorithms are symplectic,
preserve the momentum map associated with a Lie group of symmetries and also
describe the energy variation.Comment: 8 page
Towards a Hamilton-Jacobi Theory for Nonholonomic Mechanical Systems
In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical
systems. The results are applied to a large class of nonholonomic mechanical
systems, the so-called \v{C}aplygin systems.Comment: 13 pages, added references, fixed typos, comparison with previous
approaches and some explanations added. To appear in J. Phys.
Quasivelocities and Optimal Control for Underactuated Mechanical Systems
This paper is concerned with the application of the theory of quasivelocities
for optimal control for underactuated mechanical systems. Using this theory, we
convert the original problem in a variational second-order lagrangian system
subjected to constraints. The equations of motion are geometrically derived
using an adaptation of the classical Skinner and Rusk formalism.Comment: 8 page
Reduced classical field theories. k-cosymplectic formalism on Lie algebroids
In this paper we introduce a geometric description of Lagrangian and
Hamiltonian classical field theories on Lie algebroids in the framework of
-cosymplectic geometry. We discuss the relation between Lagrangian and
Hamiltonian descriptions through a convenient notion of Legendre
transformation. The theory is a natural generalization of the standard one; in
addition, other interesting examples are studied, mainly on reduction of
classical field theories.Comment: 26 page
Discrete variational integrators and optimal control theory
A geometric derivation of numerical integrators for optimal control problems
is proposed. It is based in the classical technique of generating functions
adapted to the special features of optimal control problems.Comment: 17 page
Tulczyjew's triples and lagrangian submanifolds in classical field theories
In this paper the notion of Tulczyjew's triples in classical mechanics is
extended to classical field theories, using the so-called multisymplectic
formalism, and a convenient notion of lagrangian submanifold in multisymplectic
geometry. Accordingly, the dynamical equations are interpreted as the local
equations defining these lagrangian submanifolds.Comment: 29 page
Singular lagrangian systems and variational constrained mechanics on Lie algebroids
The purpose of this paper is describe Lagrangian Mechanics for constrained
systems on Lie algebroids, a natural framework which covers a wide range of
situations (systems on Lie groups, quotients by the action of a Lie group,
standard tangent bundles...). In particular, we are interested in two cases:
singular Lagrangian systems and vakonomic mechanics (variational constrained
mechanics). Several examples illustrate the interest of these developments.Comment: 42 pages, Section with examples improve
Geometric numerical integration of nonholonomic systems and optimal control problems
A geometric derivation of numerical integrators for nonholonomic systems and
optimal control problems is obtained. It is based in the classical technique of
generating functions adapted to the special features of nonholonomic systems
and optimal control problems.Comment: 6 pages, 1 figure. Submitted to IFAC Workshop on Lagrangian and
Hamiltonian Methods for Nonlinear Control, Sevilla 200
A new geometric setting for classical field theories
A new geometrical setting for classical field theories is introduced. This
description is strongly inspired in the one due to Skinner and Rusk for
singular lagrangians systems. For a singular field theory a constraint
algorithm is developed that gives a final constraint submanifold where a
well-defined dynamics exists. The main advantage of this algorithm is that the
second order condition is automatically included.Comment: 22 page
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