Nonholonomic mapping theory of autoparallel motions in Riemann-Cartan space  

作　　者：GUO YongXin1,LIU Chang2,WANG Yong3,LIU ShiXing1 & CHANG Peng2 1 College of Physics,Liaoning University,Shenyang 110036,China 2 School of Aerospace Engineering,Beijing Institute of Technology,Beijing 110081,China 3 School of Basic Medical Science,Guangdong Medical College,Dongguan 523808,China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2010年第9期1707-1715,共9页中国科学：物理学、力学、天文学（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 Province of China (Grant No 2008S098);the Program Supporting Elitists of Higher Education of Liaoning Province of China (Grant No 2008RC20);the Program of Constructing Liaoning Provincial Key Laboratory of China (Grant No 2008403009)

摘　　要：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 Weitzenbck 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 Weitzenbck 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.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 Weitzenbck 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 Weitzenbck 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.

关 键 词：NONHOLONOMIC MAPPING Riemann-Cartan SPACE connection torsion autoparallel 

分 类 号：O302[理学—力学]