Quasi-momentum theorem in Riemann-Cartan space
Quasi-momentum theorem in Riemann-Cartan space
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DOI：
10.1007/s10483-018-2323-6
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发表时间：
2018-01
影响因子：
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通讯作者：
Yong Wang;Changyang Liu;Jing Xiao;F. Mei
中科院分区：
文献类型：
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作者：
Yong Wang;Changyang Liu;Jing Xiao;F. Mei
利用非完整映射理论，研究了一阶线性齐次硬性非完整系统在作用力作用下的运动几何方程。在Riemann-Cartan位形空间中得到了动力系统的拟牛顿定律、拟动量定理和第二类拉格朗日方程。通过非完整映射，动力学系统的欧几里得位形空间或黎曼位形空间可以映射到有挠度的黎曼-卡坦位形空间。通过拟牛顿定律或拟动量定理，可在其Riemann-Cartan位形空间中得到动力学系统的运动微分方程。对于约束系统，其Riemann-Cartan位形空间中的运动微分方程可能比其欧几里德位形空间或Riemann位形空间中的运动方程简单。因此，非完整映射理论可以解决一些用传统分析力学方法难以解决的约束问题。给出了三个算例，说明了该方法的有效性。
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 Riemann-Cartan 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.