GEOMETRIC HAMILTON–JACOBI THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS-Reference-Cited by-同舟云学术

GEOMETRIC HAMILTON–JACOBI THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS

Published:2010-05 Issue:03 Volume:07 Page:431-454
ISSN:0219-8878
Container-title:International Journal of Geometric Methods in Modern Physics
language:en
Short-container-title:Int. J. Geom. Methods Mod. Phys.

Author:

CARIÑENA JOSÉ F.¹,GRÀCIA XAVIER²,MARMO GIUSEPPE³⁴,MARTÍNEZ EDUARDO⁵,MUÑOZ-LECANDA MIGUEL C.⁶,ROMÁN-ROY NARCISO⁶

Affiliation:

1. Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

2. Departamento de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, Campus Nord UPC, Ed. C3, C. Jordi Girona 1, 08034 Barcelona, Catalonia, Spain

3. Dipartimento di Scienze Fisiche, Universitá Federico II di Napoli, Via Cintia, 80126 Napoli, Italy

4. INFN, Sezione di Napoli, Complesso Univ. di Monte Sant'Angelo, Via Cintia, 80126 Napoli, Italy

5. Departamento de Matemática Aplicada and IUMA, Facultad de Ciencias, Univ. de Zaragoza, 50009 Zaragoza, Spain

6. Departamento de Matemática Aplicada IV, Universidad Politécnica de Cataluña, Campus Nord UPC, Ed. C3, C. Jordi Girona 1, 08034 Barcelona, Spain

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219887810004385

Reference29 articles.

1. Control Theory from the Geometric Viewpoint

2. Mathematical Methods of Classical Mechanics

3. Nonholonomic reduction

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