Gauss Principle of Least Compulsion for Relative Motion Dynamics and Differential Equations of Motion  

作　　者：ZHANG Yi XIA Junling 

机构地区：[1]College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,Jiangsu,China

出　　处：《Wuhan University Journal of Natural Sciences》2024年第3期273-283,共11页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China (12272248, 11972241)。

摘　　要：This paper focuses on Gauss principle of least compulsion for relative motion dynamics and derives differential equations of motion from it. Firstly, starting from the dynamic equation of the relative motion of particles, we give the Gauss principle of relative motion dynamics. By constructing a compulsion function of relative motion, we prove that at any instant, its real motion minimizes the compulsion function under Gaussian variation, compared with the possible motions with the same configuration and velocity but different accelerations. Secondly, the formula of acceleration energy and the formula of compulsion function for relative motion are derived because the carried body is rigid and moving in a plane. Thirdly, the Gauss principle we obtained is expressed as Appell, Lagrange, and Nielsen forms in generalized coordinates. Utilizing Gauss principle, the dynamical equations of relative motion are established. Finally, two relative motion examples also verify the results' correctness.

关 键 词：relative motion dynamics Gauss principle of least compulsion acceleration energy compulsion function 

分 类 号：O316[理学—一般力学与力学基础]