scholarly journals Lie symmetry and Hojman conserved quantity of Nielsen equation in a dynamical system of the relative motion

2011 ◽  
Vol 60 (3) ◽  
pp. 030201
Author(s):  
Xie Yin-Li ◽  
Jia Li-Qun ◽  
Yang Xin-Fang
Keyword(s):  
Dynamical System ◽  
Relative Motion ◽  
Lie Symmetry ◽  
Conserved Quantity ◽  
Hojman Conserved Quantity

Lie Symmetry and Approximate Hojman Conserved Quantity of Lagrange Equations for a Weakly Nonholonomic System

2013 ◽  
Vol 30 (1) ◽  
pp. 21-27 ◽  
Author(s):  
Y.-L. Han ◽  
X.-X. Wang ◽  
M.-L. Zhang ◽  
L.-Q. Jia
Keyword(s):  
Nonholonomic System ◽  
Equations Of Motion ◽  
Lie Symmetry ◽  
Conserved Quantity ◽  
Holonomic System ◽  
Lagrange Equations ◽  
Definition Of ◽  
Weakly Nonholonomic System ◽  
Infinitesimal Transformations ◽  
Hojman Conserved Quantity

ABSTRACTThe Lie symmetry and Hojman conserved quantity of Lagrange equations for a weakly nonholonomic system and its first-degree approximate holonomic system are studied. The differential equations of motion for the system are established. Under the special infinitesimal transformations of group in which the time is invariable, the definition of the Lie symmetry for the weakly nonholonomic system and its first-degree approximate holonomic system are given, and the exact and approximate Hojman conserved quantities deduced directly from the Lie symmetry are obtained. Finally, an example is given to study the exact and approximate Hojman conserved quantity for the system.

Lie symmetry and Hojman conserved quantity of Nambu system

2008 ◽  
Vol 17 (12) ◽  
pp. 4361-4364 ◽  
Author(s):  
Lin Peng ◽  
Fang Jian-Hui ◽  
Pang Ting
Keyword(s):  
Lie Symmetry ◽  
Conserved Quantity ◽  
Hojman Conserved Quantity
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