Second form of the generalized Hamilton-Jacobi method for nonholonomic dynamical systems

1978 ◽  
Vol 29 (5) ◽  
pp. 828-834 ◽  
Author(s):  
René Dooren
Keyword(s):  
Dynamical Systems ◽  
Jacobi Method ◽  
Nonholonomic Dynamical Systems

The Hamilton-Jacobi method for arbitrary rheo-linear dynamical systems

2003 ◽  
Vol 163 (1) ◽  
pp. 51-79
Author(s):  
B. S. Bačlić ◽  
B. D. Vujanović
Keyword(s):  
Dynamical Systems ◽  
Jacobi Method ◽  
Linear Dynamical Systems

Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

2008 ◽  
Vol 372 (10) ◽  
pp. 1555-1561 ◽  
Author(s):  
Jingli Fu ◽  
Salvador Jiménez ◽  
Yifa Tang ◽  
Luis Vázquez
Keyword(s):  
Dynamical Systems ◽  
Time Dependent ◽  
Nonholonomic Dynamical Systems

Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems

2003 ◽  
Vol 12 (7) ◽  
pp. 695-699 ◽  
Author(s):  
Fu Jing-Li ◽  
Chen Li-Qun ◽  
Bai Jing-Hua ◽  
Yang Xiao-Dong
Keyword(s):  
Dynamical Systems ◽  
Lie Symmetries ◽  
Conserved Quantities ◽  
Nonholonomic Dynamical Systems

scholarly journals GEOMETRIC HAMILTON–JACOBI THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS

2010 ◽  
Vol 07 (03) ◽  
pp. 431-454 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
XAVIER GRÀCIA ◽  
GIUSEPPE MARMO ◽  
EDUARDO MARTÍNEZ ◽  
MIGUEL C. MUÑOZ-LECANDA ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Symplectic Structure ◽  
Free Particle ◽  
Nonholonomic Constraints ◽  
Lagrangian Function ◽  
Constants Of Motion ◽  
Geometric Formulation ◽  
Complete Solutions ◽  
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.

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