3,257 research outputs found

    Towards a Hamilton-Jacobi Theory for Nonholonomic Mechanical Systems

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    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

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    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

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    In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of kk-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

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    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

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    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

    A new geometric setting for classical field theories

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    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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