Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems |
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| Authors: | Zhang Ming-Jiang Fang Jian-Hui Lu Kai Zhang Ke-Jun and Li Yan |
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| Affiliation: | College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China |
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| Abstract: | This paper studies conformal invariance and conserved
quantity of third-order Lagrange equations for non-conserved
mechanical systems. Third-order Lagrange equations, the definition
and a determining equation of conformal invariance of the system are
presented. The conformal factor expression is deduced from conformal
invariance and Lie symmetry. The necessary and sufficient condition
that conformal invariance of the system would have Lie symmetry under
single-parameter infinitesimal transformations is obtained. The
corresponding conserved quantity of conformal invariance is derived
with the aid of a structure equation. Lastly, an example is given to
illustrate the application of the results. |
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| Keywords: | conformal invariance conserved quantity third-order
Lagrange equation non-conserved mechanical system |
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