Open AccessExact invariants and adiabatic invariants for nonholonomic systems in non-Chetaev's type based on El-Nabulsi dynamical models
Author(s) -
Chen Ju,
Zhang Yi
Publication year - 2015
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.64.034502
Subject(s) - nonholonomic system , adiabatic process , adiabatic invariant , physics , invariant (physics) , noether's theorem , dynamical systems theory , mathematical physics , symmetry (geometry) , classical mechanics , type (biology) , homogeneous space , differential equation , equations of motion , mathematics , lagrangian , quantum mechanics , computer science , geometry , ecology , artificial intelligence , robot , mobile robot , biology
In this paper, the problem of exact invariants and adiabatic invariants for nonholonomic system in non-Chetaev's type based on the El-Nabulsi dynamical model is studied. First, the El-Nabulsi-d'Alembert-Lagrange principle is deduced and the differential equations of motion of the system are established. Then, the relation between the Noether symmetry and the exact invariant that is led directly by the symmetry for undisturbed nonholonomic system in non-Chetaev's type is given. Furthermore, by introducing the concept of high-order adiabatic invariant of a mechanical system, the conditions that the perturbation of symmetry leads to the adiabatic invariant and its formulation are studied for the nonholonomic system in non-Chetaev's type under the action of small disturbance. As a special case, the problem of the exact invariants and the adiabatic invariants for the nonholonomic system in Chetaev's type in El-Nabulsi model is discussed. At the end of the paper, two examples for the nonholonomic systems in non-Chetaev's type constraints and also the Chetaev's type constraints are given respectively to show the application of the methods and the results of this paper.