Nondeterminacy of dynamics, i.e., the nonholonomic or the vakonomic, fundamental variational principles, e.g. ...
Yong-Xin Guo and Shi-Xing Liu Physics College, Liaoning University, Shenyang 110036, ChinaChang Liu Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China
The method of nonholonomic mapping is utilized to construct a Riemann-Cartan space embedded into a known Riemann-Cartan space,which includes two special cases that a Weitzenbck space and a Riemann-Cartan space are respectively embedded into a Euclidean space and a Riemann space.By means of this mapping theory,the nonholonomic corresponding relation between the autoparallels of two Riemman-Cartan spaces is investigated.In particular,an autoparallel in a Riemann-Cartan space can be mapped into a geodesic line in a Riemann space and an autoparallel in Weitzenbck space be mapped into a geodesic line in Euclidean space.Based on the Lagrange-d'Alembert principle,the equations of motion for dynamical systems in Riemman-Cartan space should be autoparallel equations of the space.As applications,the problem of autoparallel motion of spinless particles,Chaplygin's nonholonomic systems and a rigid body rotating with a fixed point are investigated in space with torsion.
GUO YongXin1,LIU Chang2,WANG Yong3,LIU ShiXing1 & CHANG Peng2 1 College of Physics,Liaoning University,Shenyang 110036,China
Nondeterminacy of dynamics, i.e., the nonholonomic or the vakonomic, fundamental variational principles, e.g. ...
Yong-Xin Guo and Shi-Xing Liu Physics College, Liaoning University, Shenyang 110036, ChinaChang Liu Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China
Based on the Cauchy-Kovalevski theorem for a system of partial dierential equations to be integrable,a kind of...
Yong-Xin Guo1)Chang Liu2)Shi-Xing Liu1)1College of Physics,Liaoning University,Shenyang 110036,China 2School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China
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.
