scholarly journals Conformal invariance and conserved quantities of Mei symmetry for general holonomic systems

2009 ◽  
Vol 58 (1) ◽  
pp. 22
Author(s):  
Cai Jian-Le
Keyword(s):  
Conformal Invariance ◽  
Conserved Quantities ◽  
Holonomic Systems ◽  
Mei Symmetry

Conformal Invariance and Conserved Quantity of the Higher-Order Holonomic Systems by Lie Point Transformation

2012 ◽  
Vol 28 (3) ◽  
pp. 589-596 ◽  
Author(s):  
J.-L. Cai ◽  
F.-X. Mei
Keyword(s):  
Conformal Invariance ◽  
Infinitesimal Generator ◽  
Transformation Group ◽  
Equation Of Motion ◽  
Higher Order ◽  
Lie Symmetry ◽  
Point Transformation ◽  
Conserved Quantities ◽  
Holonomic Systems ◽  
Parameter Point

AbstractIn this paper, the conformal invariance and conserved quantities for higher-order holonomic systems are studied. Firstly, by establishing the differential equation of motion for the systems and introducing a one-parameter infinitesimal transformation group together with its infinitesimal generator vector, the determining equation of conformal invariance for the systems are provided, and the conformal factors expression are deduced. Secondly, the relation between conformal invariance and the Lie symmetry by the infinitesimal one-parameter point transformation group for the higher-order holonomic systems are deduced. Thirdly, the conserved quantities of the systems are derived using the structure equation satisfied by the gauge function. Lastly, an example of a higher-order holonomic mechanical system is discussed to illustrate these results.

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