Downloads provided by UsageCountsGEOMETRIC HAMILTON–JACOBI THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS
Copyright policy ) Cariñena, José F.; Gràcia Sabaté, Francesc Xavier; Marmo, Giuseppe; Martínez, Eduardo; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso;
GEOMETRIC HAMILTON–JACOBI THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS
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.
and methods, Nonholonomic Lagrangian system, Lagrange, Funcions de, Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics, Hamilton–Jacobi equation, :37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory [Classificació AMS], :34 Ordinary differential equations::34A General theory [Classificació AMS], Hamilton, Equacions diferencials ordinàries, and nonholonomic systems, Lagrangian, Mathematical Physics, approaches, :37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [Classificació AMS], Mathematical Physics (math-ph), Sistemes dinàmics diferenciables, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, Dynamics, Sistemes de, Lagrangian functions, Quasivelocity, :70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics [Classificació AMS], including celestial mechanics, Classificació AMS::34 Ordinary differential equations::34A General theory, contact, Differential equations, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria, Symplectic manifold, FOS: Physical sciences, Mechanics, Partícules (Física nuclear), Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, :70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics [Classificació AMS], Differentiable dynamical systems, Constant of motion, Hamiltonian systems, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems, :70 Mechanics of particles and systems::70G General models, approaches, and methods [Classificació AMS], Lagrange, Classificació AMS::70 Mechanics of particles and systems::70G General models, Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods, Funcions de, Complete integral, Hamilton, Sistemes de, Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics, :Matemàtiques i estadística::Geometria [Àrees temàtiques de la UPC], Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, 34A26, 37C1, 37J60, 70F25, 70G45, 70H03, 70H05, 70H20
and methods, Nonholonomic Lagrangian system, Lagrange, Funcions de, Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics, Hamilton–Jacobi equation, :37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory [Classificació AMS], :34 Ordinary differential equations::34A General theory [Classificació AMS], Hamilton, Equacions diferencials ordinàries, and nonholonomic systems, Lagrangian, Mathematical Physics, approaches, :37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [Classificació AMS], Mathematical Physics (math-ph), Sistemes dinàmics diferenciables, Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory, Dynamics, Sistemes de, Lagrangian functions, Quasivelocity, :70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics [Classificació AMS], including celestial mechanics, Classificació AMS::34 Ordinary differential equations::34A General theory, contact, Differential equations, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria, Symplectic manifold, FOS: Physical sciences, Mechanics, Partícules (Física nuclear), Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, :70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics [Classificació AMS], Differentiable dynamical systems, Constant of motion, Hamiltonian systems, Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems, :70 Mechanics of particles and systems::70G General models, approaches, and methods [Classificació AMS], Lagrange, Classificació AMS::70 Mechanics of particles and systems::70G General models, Classificació AMS::70 Mechanics of particles and systems::70G General models, approaches, and methods, Funcions de, Complete integral, Hamilton, Sistemes de, Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics, :Matemàtiques i estadística::Geometria [Àrees temàtiques de la UPC], Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, 34A26, 37C1, 37J60, 70F25, 70G45, 70H03, 70H05, 70H20
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