| Issue |
Wuhan Univ. J. Nat. Sci.
Volume 29, Number 2, April 2024
|
|
|---|---|---|
| Page(s) | 106 - 116 | |
| DOI | https://doi.org/10.1051/wujns/2024292106 | |
| Published online | 14 May 2024 | |
Mathematics
CLC number: O316
Canonical Transformations and Poisson Theory for Dynamics with Non-Standard Lagrangians
1
School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China
2
School of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, Jiangsu, China
† Corresponding author. E-mail: zhy@mail.usts.edu.cn
Received:
8
June
2023
The canonical transformation and Poisson theory of dynamical systems with exponential, power-law, and logarithmic non-standard Lagrangians are studied, respectively. The criterion equations of canonical transformation are established, and four basic forms of canonical transformations are given. The dynamic equations with non-standard Lagrangians admit Lie algebraic structure. From this, we establish the Poisson theory, which makes it possible to find new conservation laws through known conserved quantities. Some examples are put forward to demonstrate the use of the theory and verify its effectiveness.
Key words: non-standard Lagrangians / dynamical equations / canonical transformation / Poisson theory
Cite this article: ZHU Lin, ZHANG Yi. Canonical Transformations and Poisson Theory for Dynamics with Non-Standard Lagrangians[J]. Wuhan Univ J of Nat Sci, 2024, 29(2): 106-116.
Biography: ZHU Lin, female, Master candidate, research direction: analytical mechanics. E-mail: 649405840@qq.com
Fundation item: Supported by the National Natural Science Foundation of China (12272248, 11972241)
© Wuhan University 2024
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