Two formulations and solutions of the inverse problems for Lie symmetries in dynamics of a Birkhoffian system

LONG Zi-xuan; ZHANG Yi

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May 2012

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LONG Zi-xuan, ZHANG Yi. Two formulations and solutions of the inverse problems for Lie symmetries in dynamics of a Birkhoffian system[J]. Journal of East China Normal University (Natural Sciences), 2012, (3): 49-55.

Citation:

LONG Zi-xuan, ZHANG Yi. Two formulations and solutions of the inverse problems for Lie symmetries in dynamics of a Birkhoffian system[J]. Journal of East China Normal University (Natural Sciences), 2012, (3): 49-55.

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Two formulations and solutions of the inverse problems for Lie symmetries in dynamics of a Birkhoffian system

LONG Zi-xuan¹,
ZHANG Yi²

1.
College of Mathematics and Physics, Suzhou University of Science and Technology, Jiangsu 215009, China;
2.
College of Civil Engineering, Suzhou University of

Received Date: 2011-06-01
Rev Recd Date: 2011-09-01
Publish Date: 2012-05-25

Abstract

Abstract

First, the determining equations, the structure equations and the conserved quantities of Lie symmetries for a Birkhoffian system were given; then two formulations and solutions of the inverse problems of Lie symmetries for the system were presented. The results show that the same Birkhoffian(Birkhoff's functions) and first integral can correspond to different Birkhoff's functions(Birkhoffian) and different Lie symmetries, and can also correspond to the same Lie symmetry and different Birkhoff's functions(Birkhoffian).
- Birkhoffian system,
- Lie symmetry,
- inverse problem

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References(1)

References

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