Geometric Hamilton-Jacobi Theory for Nonholonomic Dynamical Systems

Abstract

The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the symplectic structure defined from the Lagrangian function and the constraints is studied. The concept of complete solutions and their relationship with constants of motion, are also studied in detail. Local expressions using quasivelocities are provided. As an example, the nonholonomic free particle is considered.

22 pp

References in corpus (6)

• Lagrangian submanifolds and dynamics on Lie algebroids
• Geometric Hamilton-Jacobi Theory
• A Geometric Hamilton-Jacobi Theory for Classical Field Theories
• Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic Mechanics
• A Lie algebroid framework for non-holonomic systems
• Regularity and symmetries of nonholonomic systems

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• On the role of geometry in statistical mechanics and thermodynamics I: Geometric perspective
• Hamilton-Jacobi theory in k-cosymplectic field theories
• Geometric Hamilton-Jacobi theory for higher-order autonomous systems
• On the Hamilton-Jacobi Theory for Singular Lagrangian Systems
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• Structural aspects of Hamilton-Jacobi theory
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• Hamilton-Jacobi theory in multisymplectic classical field theories
• A new perspective on nonholonomic brackets and Hamilton-Jacobi theory
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• Reduction of a Hamilton-Jacobi equation for nonholonomic systems
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• Hamilton-Jacobi Equations for Nonholonomic Reducible Hamiltonian Systems on a Cotangent Bundle
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• Hamilton-Jacobi Equations of Nonholonomic Magnetic Hamiltonian Systems
• Hamilton-Jacobi Theorems for Regular Reducible Hamiltonian Systems on a Cotangent Bundle