scholarly journals Routh equation of nonholonomic dynamical systems: from Chetaev condition to Euler condition

2005 ◽  
Vol 54 (6) ◽  
pp. 2468
Author(s):  
Shen Hui-Chuan
Keyword(s):  
Dynamical Systems ◽  
Nonholonomic 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.

scholarly journals Topology and Bifurcations in Nonholonomic Mechanics

2015 ◽  
Vol 25 (10) ◽  
pp. 1530028 ◽  
Author(s):  
Ivan A. Bizyaev ◽  
Alexey Bolsinov ◽  
Alexey Borisov ◽  
Ivan Mamaev
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Qualitative Analysis ◽  
Poisson Bracket ◽  
Nonholonomic Mechanics ◽  
Hamiltonian Form ◽  
Topological Methods ◽  
Integral Manifolds ◽  
Nonholonomic Dynamical Systems

This paper develops topological methods for qualitative analysis of the behavior of nonholonomic dynamical systems. Their application is illustrated by considering a new integrable system of nonholonomic mechanics, called a nonholonomic hinge. Although this system is nonholonomic, it can be represented in Hamiltonian form with a Lie–Poisson bracket of rank two. This Lie–Poisson bracket is used to perform stability analysis of fixed points. In addition, all possible types of integral manifolds are found and a classification of trajectories on them is presented.

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