A new type of adiabatic invariants for disturbed non-conservative nonholonomic system  

作　　者：Xin-Xin Xu Yi Zhang 徐鑫鑫;张毅(College of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou 215009,China;College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)

机构地区：[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

出　　处：《Chinese Physics B》2019年第12期118-122,共5页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11572212,11272227,and 10972151);the Innovation Program for Postgraduade in Higher Education Institutions of Jiangsu Province,China(Grant No.KYCX18_2548)

摘　　要：According to the Herglotz variational principle and differential variational principle of Herglotz type, we study the adiabatic invariants for a non-conservative nonholonomic system. Firstly, the differential equations of motion of the non-conservative nonholonomic system based upon the generalized variational principle of Herglotz type are given, and the exact invariant for the non-conservative nonholonomic system is introduced. Secondly, a new type of adiabatic invariant for the system under the action of a small perturbation is obtained. Thirdly, the inverse theorem of the adiabatic invariant is given. Finally, an example is given.According to the Herglotz variational principle and differential variational principle of Herglotz type, we study the adiabatic invariants for a non-conservative nonholonomic system. Firstly, the differential equations of motion of the non-conservative nonholonomic system based upon the generalized variational principle of Herglotz type are given, and the exact invariant for the non-conservative nonholonomic system is introduced. Secondly, a new type of adiabatic invariant for the system under the action of a small perturbation is obtained. Thirdly, the inverse theorem of the adiabatic invariant is given. Finally, an example is given.

关 键 词：non-conservative nonholonomic mechanics adiabatic invariants differential variational principle of Herglotz type 

分 类 号：O17[理学—数学]