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Exact invariants and adiabatic invariants for nonholonomic systems in non-Chetaev's type based on El-Nabulsi dynamical models

Chen Ju Zhang Yi

Exact invariants and adiabatic invariants for nonholonomic systems in non-Chetaev's type based on El-Nabulsi dynamical models

Chen Ju, Zhang Yi
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Publishing process
  • Received Date:  11 July 2014
  • Accepted Date:  11 August 2014
  • Published Online:  05 February 2015

Exact invariants and adiabatic invariants for nonholonomic systems in non-Chetaev's type based on El-Nabulsi dynamical models

  • 1. College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
  • 2. College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos.10972151, 11272227), the Scientific Research and Innovation Program for the Graduate Students in Institution of Higher Education of Jiangsu Province, China (Grant No. CXLX13-855), and the Scientific Research and Innovation Program for the Graduate Students of Suzhou University of Science and Technology, China (Grant No. SKCX13S-050).

Abstract: 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.

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