Inverse problem for Chaplygin’s nonholonomic systems  

作　　者：LIU Chang LIU ShiXing GUO 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)》2011年第8期2100-2106,共7页中国科学（技术科学英文版）

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：nonholonomic constraints inverse problems Birkhoff’s equations geonotopic transformations conditions of self-adjointness 

分 类 号：O316[理学—一般力学与力学基础] O171[理学—力学]