Abstract Based on the theory of Lie symmetries and conserved quantities, the exact invariants and adiabatic invariants of holonomic system are studied in terms of quasi-coordinates. The perturbation to symmetries for the holonomic system in terms of quasi-coordinates under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
Received: 10 October 2004
Revised: 02 November 2004
Accepted manuscript online:
PACS:
45.05.+x
(General theory of classical mechanics of discrete systems)
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10372053); the Natural Science Foundation of Henan Province, China(Grant No 0311010900), and the Foundation of Young Key Member of the Teachers in Institutions of Higher Learning of Henan Province, China.
Cite this article:
Chen Xiang-Wei (陈向炜), Li Yan-Min (李彦敏) Exact invariants and adiabatic invariants of holonomic system in terms of quasi-coordinates 2005 Chinese Physics 14 663
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