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| Perturbation to Mei symmetry and Mei adiabatic invariants for mechanical systems in phase space |
| Zhang Ming-Jiang, Fang Jian-Hui, Zhang Xiao-Ni, Lu Kai |
| College of Physics Science and Technology, China University
of Petroleum, Dongying 257061, China |
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Abstract For a perturbed mechanical system in phase space, considering
${\tilde{{\rm d}}}/{ {{\rm d}t}}$ in the structure equation and
process of proof including infinitesimal parameter $\varepsilon $
obviously, this paper studies the perturbation to Mei symmetry and
adiabatic invariants. Firstly, the exact invariant induced directly
from the Mei symmetry of the system without perturbation is given.
Secondly, based on the concept of high-order adiabatic invariant,
the determining equations of the perturbation to Mei symmetry are
established, the condition of existence of the Mei adiabatic
invariant led by the perturbation to Mei symmetry is obtained, and
its form is presented. Lastly, an example is given to illustrate the
application of the results.
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Received: 17 August 2007
Published: 20 June 2008
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| PACS: |
45.20.Jj
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(Lagrangian and Hamiltonian mechanics)
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02.30.Jr
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(Partial differential equations)
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2008, Vol. 17 
