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

Published online by Cambridge University Press:  09 August 2012

J.-L. Cai  and
F.-X. Mei
J.-L. Cai*
Affiliation:
College of Science, Hangzhou Normal University Hangzhou, 310018, China
F.-X. Mei
Affiliation:
College of Science, Beijing Institute of Technology, Beijing, 100081, China
*
*Corresponding author ([email protected])
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Abstract

In 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.

Keywords

Higher-order holonomic systemLie point transformationConformal invarianceDetermining equationConserved quantity
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 3 , September 2012 , pp. 589 - 596
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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