Open AccessPerturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical system in phase place
Author(s) -
Lili Xia,
Li Yuan-Cheng
Publication year - 2007
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.56.6183
Subject(s) - adiabatic invariant , adiabatic process , homogeneous space , nonholonomic system , perturbation (astronomy) , phase space , invariant (physics) , mechanical system , physics , classical mechanics , mathematical physics , mathematics , computer science , quantum mechanics , geometry , robot , artificial intelligence , mobile robot
This paper studies the perturbation to symmetries and the adiabatic invariant for nonholonomic controllable mechanical system in the phase space. The exact invariants introduced by the form invariance of the nonholonomic controllable mechanical system in phase space without perturbation are given. Based on the definition of high-order adiabatic invariants of the mechanical system, the perturbation to symmetries and the adiabatic invariant for nonholonomic controllable mechanical system in phase space under the action of small disturbance is investigated, then the form of high-order adiabatic invariants and the conditions for their existence are presented. An example is finally given to illustrate the application of the results.