Issue |
Wuhan Univ. J. Nat. Sci.
Volume 29, Number 3, June 2024
|
|
---|---|---|
Page(s) | 273 - 283 | |
DOI | https://doi.org/10.1051/wujns/2024293273 | |
Published online | 03 July 2024 |
Mathematics
CLC number: O316
Gauss Principle of Least Compulsion for Relative Motion Dynamics and Differential Equations of Motion
College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, Jiangsu, China
Received:
31
July
2023
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.
Key words: relative motion dynamics / Gauss principle of least compulsion / acceleration energy / compulsion function
Cite this article: ZHANG Yi, XIA Junling. Gauss Principle of Least Compulsion for Relative Motion Dynamics and Differential Equations of Motion[J]. Wuhan Univ J of Nat Sci, 2024, 29(3): 273-283.
Biography: ZHANG Yi, male, Ph.D., Professor, research direction: analytical mechanics. E-mail: zhy@mail.usts.edu.cn
Fundation item: Supported by the National Natural Science Foundation of China (12272248, 11972241)
© Wuhan University 2024
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