scholarly journals Approximate conserved quantity of a weakly nonholonomic system

2009 ◽  
Vol 58 (10) ◽  
pp. 6729
Author(s):  
Ge Wei-Kuan
Keyword(s):  
Nonholonomic System ◽  
Conserved Quantity ◽  
Approximate Conserved Quantity ◽  
Weakly Nonholonomic System

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.

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