Quasi-momentum theorem in Riemann-Cartan space

doi:10.1007/s10483-018-2323-6

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (5): 733-746.doi: https://doi.org/10.1007/s10483-018-2323-6

Quasi-momentum theorem in Riemann-Cartan space

Yong WANG¹, Chang LIU^3,4, Jing XIAO¹, Fengxiang MEI²

1. Department of Information Engineering, Guangdong Medical University, Dongguan 523808, Guangdong Province, China;
2. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;
3. College of Physics, Liaoning University, Shenyang 110036, China;
4. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province, China

收稿日期:2017-05-13 修回日期:2017-11-10 出版日期:2018-05-01 发布日期:2018-05-01
通讯作者: Fengxiang MEI,E-mail:meifx@bit.edu.cn E-mail:meifx@bit.edu.cn
基金资助:
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)

Quasi-momentum theorem in Riemann-Cartan space

Yong WANG¹, Chang LIU^3,4, Jing XIAO¹, Fengxiang MEI²

1. Department of Information Engineering, Guangdong Medical University, Dongguan 523808, Guangdong Province, China;
2. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;
3. College of Physics, Liaoning University, Shenyang 110036, China;
4. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province, China

Received:2017-05-13 Revised:2017-11-10 Online:2018-05-01 Published:2018-05-01
Contact: Fengxiang MEI E-mail:meifx@bit.edu.cn
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)

摘要/Abstract

摘要：

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.

关键词: Riemann-Cartan space, quasi-momentum theorem, non-holonomic system, holonomic system, the Hamilton, nonholonomic system, nonholonomic mapping

Abstract:

Key words: non-holonomic system, holonomic system, the Hamilton, Riemann-Cartan space, quasi-momentum theorem, nonholonomic system, nonholonomic mapping

中图分类号:

53B20

Yong WANG, Chang LIU, Jing XIAO, Fengxiang MEI. Quasi-momentum theorem in Riemann-Cartan space[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(5): 733-746.

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Quasi-momentum theorem in Riemann-Cartan space

Quasi-momentum theorem in Riemann-Cartan space

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