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 ...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.展开更多
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)+2 种基金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)
文摘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.
