11,414 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.
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
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
Simulating Nonholonomic Dynamics
This paper develops different discretization schemes for nonholonomic
mechanical systems through a discrete geometric approach. The proposed methods
are designed to account for the special geometric structure of the nonholonomic
motion. Two different families of nonholonomic integrators are developed and
examined numerically: the geometric nonholonomic integrator (GNI) and the
reduced d'Alembert-Pontryagin integrator (RDP). As a result, the paper provides
a general tool for engineering applications, i.e. for automatic derivation of
numerically accurate and stable dynamics integration schemes applicable to a
variety of robotic vehicle models
Constrained Variational Calculus for Higher Order Classical Field Theories
We develop an intrinsic geometrical setting for higher order constrained
field theories. As a main tool we use an appropriate generalization of the
classical Skinner-Rusk formalism. Some examples of application are studied, in
particular, applications to the geometrical description of optimal control
theory for partial differential equations.Comment: 25 pages; 4 diagram
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