Applied Mathematics and Mechanics >
Quasi-momentum theorem in Riemann-Cartan space
Received date: 2017-05-13
Revised date: 2017-11-10
Online published: 2018-05-01
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 11772144, 11572145, 11472124, 11572034, and 11202090), the Science and Technology Research Project of Liaoning Province (No. L2013005), the China Postdoctoral Science Foundation (No. 2014M560203), and the Natural Science Foundation of Guangdong Provience (No. 2015A030310127)
The geometric formulation of motion of the first-order linear homogenous scleronomous nonholonomic system subjected to active forces is studied with the nonholonomic mapping theory. The quasi-Newton law, the quasi-momentum theorem, and the second kind Lagrange equation of dynamical systems are obtained in the RiemannCartan configuration spaces. By the nonholonomic mapping, a Euclidean configuration space or a Riemann configuration space of a dynamical system can be mapped into a Riemann-Cartan configuration space with torsion. The differential equations of motion of the dynamical system can be obtained in its Riemann-Cartan configuration space by the quasi-Newton law or the quasi-momentum theorem. For a constrained system, the differential equations of motion in its Riemann-Cartan configuration space may be simpler than the equations in its Euclidean configuration space or its Riemann configuration space. Therefore, the nonholonomic mapping theory can solve some constrained problems, which are difficult to be solved by the traditional analytical mechanics method. Three examples are given to illustrate the effectiveness of the method.
Yong WANG, Chang LIU, Jing XIAO, Fengxiang MEI . Quasi-momentum theorem in Riemann-Cartan space[J]. Applied Mathematics and Mechanics, 2018 , 39(5) : 733 -746 . DOI: 10.1007/s10483-018-2323-6
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