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This paper studies the exact invariants and the adiabatic invariants for systems of generalized classical mechanics in the high-dimensional extended phase space and gives the relations between the invariants and the symmetries of the system s in the space. Based on the concept of high-order adiabatic invariant of mechan ical systems with the action of small disturbance, it presents the form of the h igh-order adiabatic invariant and the conditions for their existence,and establi shes the relationship between adiabatic invariant and symmetrical transformation . In the end of this paper, an example is given to illustrate the application of the results.
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Keywords:
- symmetry /
- perturbation /
- invariant /
- system of generalized classical mechanics /
- ex tended phase space
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