Inverse problem for Chaplygin’s nonholonomic systems

查看全文 作　　者：LIU [1,2]Chang;LIU [1,2]ShiXing;GUO [1]YongXin

机构地区：[1]College of Physics, Liaoning University, Shenyang 110036, China;[2]School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

出　　处：《Science China(Technological Sciences)》索引2011年第54卷第8期,共7页

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 10932002, 10872084, and 10472040);the Outstanding Young Talents Training Fund of Liaoning Province of China (Grant No. 3040005);the Research Program of Higher Education of Liaoning Prov- ince, China (Grant No. 2008S098);the Program of Supporting Elitists of Higher Education of Liaoning Province, China (Grant No. 2008RC20);the Program of Constructing Liaoning Provincial Key Laboratory, China (Grant No. 2008403009) 摘　　要：Chaplygin’s nonholonomic systems are familiar mechanical systems subject to unintegrable linear constraints, which can be reduced into holonomic nonconservative systems in a subspace of the original state space. The inverse problem of the calculus of variations or Lagrangian inverse problem for such systems is analyzed by making use of a reduction of the systems into new ones with time reparametrization symmetry and a genotopic transformation related with a conformal transformation. It is evident that the Lagrangian inverse problem does not have a direct universality. By meaning of a reduction of Chaplygin’s nonholonomic systems into holonomic, regular, analytic, nonconservative, first-order systems, the systems admit a Birkhoffian representation in a star-shaped neighborhood of a regular point of their variables, which is universal due to the Cauchy-Kovalevski theorem and the converse of the Poincaré lemma. 关键词：非完整系统逆问题非保守系统完整约束拉格朗日线性约束机械系统状态空间

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Inverse problem for Chaplygin’s nonholonomic systems

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