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

HOJMAN CONSERVED QUANTITIES AND LIE SYMMETRIES OF DISCRETE NON-CONSERVATIVE SYSTEMS

2009 ◽  
Vol 23 (10) ◽  
pp. 1315-1322 ◽  
Author(s):  
JING-LI FU ◽  
BEN-YONG CHEN
Keyword(s):  
Dynamical Systems ◽  
Lie Symmetry ◽  
Lie Symmetries ◽  
Conserved Quantity ◽  
Conserved Quantities ◽  
Conservative Systems ◽  
The Right ◽  
Hojman Conserved Quantity

This letter focuses on studying the theory of Hojman conserved quantity of the discrete non-conservative dynamical systems. The operators of discrete translation and discrete differentiation to the right and left are introduced in discrete non-conservative dynamical systems. The Hojman theorems, the determining equations and Hojman conserved quantities of the Lie symmetry are obtained for discrete non-conservative dynamical systems. Finally, an example is discussed to illustrate the application of the results.

scholarly journals New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries

2020 ◽  
Vol 17 (06) ◽  
pp. 2050090 ◽  
Author(s):  
Jordi Gaset ◽  
Xavier Gràcia ◽  
Miguel C. Muñoz-Lecanda ◽  
Xavier Rivas ◽  
Narciso Román-Roy
Keyword(s):  
Dynamical Systems ◽  
Mechanical Systems ◽  
Dissipative Systems ◽  
Conserved Quantities ◽  
Dynamical Equations ◽  
Lagrangian Formulations ◽  
New Form

We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian formalisms, studying their equivalence. We define several kinds of symmetries for contact dynamical systems, as well as the notion of dissipation laws, prove a dissipation theorem and give a way to construct conserved quantities. Some well-known examples of dissipative systems are discussed.

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