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Kinematic reduction and the Hamilton-Jacobi equation
"... Abstract. A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric in-terpretation of this relationship relies on new mathematical tech-niques for mechanics defined on a skew-sym ..."
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Abstract. A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric in-terpretation of this relationship relies on new mathematical tech-niques for mechanics defined on a skew-symmetric algebroid. This geometric structure allows us to describe in a simplified way the mechanics of nonholonomic systems with both control and external forces. Dedicated to Tudor Ratiu on the occasion of his 60th birthday 1.
A GEOMETRIC HAMILTON-JACOBI THEORY FOR CLASSICAL FIELD THEORIES
, 2008
"... In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for hamiltonian mechanics to the case of classical field theories in the framework of multisymplectic geometry and Ehresmann connections. ..."
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In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for hamiltonian mechanics to the case of classical field theories in the framework of multisymplectic geometry and Ehresmann connections.
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"... Abstract. In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems sub-jected to external forces, time-dependent mechanical systems...). We recover all these, in principle, dif ..."
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Abstract. In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems sub-jected to external forces, time-dependent mechanical systems...). We recover all these, in principle, different cases using a unified framework based on skew-symmetric algebroids with a distinguished
