分数非守恒奇异系统的李对称性和守恒量

IF 3.4 Q1 ENGINEERING, MECHANICAL 国际机械系统动力学学报(英文) Pub Date : 2023-09-19 DOI:10.1002/msd2.12086
Mingliang Zheng
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引用次数: 0

摘要

本文根据分数因子导数方法,研究了组态空间中分数非守恒奇异拉格朗日系统的李对称性理论。首先,利用分数因子计算分数阶微积分,并利用微分变分原理导出分数阶运动方程。其次,得到了在无穷小群变换下李对称性的判定方程和极限方程。此外,通过构造满足结构方程的规范生成函数,得到了由李对称引起的奇异拉格朗日系统的分数守恒量形式,该规范生成函数符合Noether准则方程。最后,我们给出了一个计算示例。结果表明,非守恒奇异拉格朗日系统的李对称性条件比守恒奇异系统更严格,但由于不变性约束的增加,非守恒力不改变守恒量的形式;同时,分数因子法与积分法具有很高的自然一致性,因此整数阶奇异系统理论可以很容易地推广到分数阶奇异拉格朗日系统。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Lie symmetries and conserved quantities of fractional nonconservative singular systems

In this paper, according to the fractional factor derivative method, we study the Lie symmetry theory of fractional nonconservative singular Lagrange systems in a configuration space. First, fractional calculus is calculated by using the fractional factor, and the fractional equations of motion are derived by using the differential variational principle. Second, the determining equations and the limiting equations of Lie symmetry under an infinitesimal group transformation are obtained. Furthermore, the fractional conserved quantity form of singular Lagrange systems caused by Lie symmetry is obtained by constructing a gauge-generating function that fulfills the structural equation, which conforms to the Noether criterion equation. Finally, we present an example of a calculation. The results show that the Lie symmetry condition of nonconservative singular Lagrange systems is more strict than conservative singular systems, but because of increased invariance restriction, the nonconservative forces do not change the form of conserved quantity; meanwhile, the fractional factor method has high natural consistency with the integral calculus, so the theory of integer-order singular systems can be easily extended to fractional singular Lagrange systems.

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