时间尺度上非移位Birkhoffian系统的Lie对称性定理

Pub Date : 2022-06-01 DOI:10.1051/wujns/2022273211

Jinyue Chen, Yi Zhang

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引用次数: 1

摘要

研究了具有时尺度非移变分问题的Birkhoffian系统的Lie定理，包括自由Birkhoffian系统、广义Birkhoffian系统和约束Birkhoffian系统。首先，建立了时尺度非移广义Pfaff-Birkhoff原理，推导了三种birkhoff系统在非移变分问题下的动力学方程。然后，在时间尺度非位移变分问题中，通过引入无穷小变换，分别定义了自由Birkhoffian系统、广义Birkhoffian系统和约束Birkhoffian系统的Lie对称性。然后推导并证明了三类Birkhoffian系统的Lie对称性定理。最后，给出了三个实例来说明结果的应用。

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Lie Symmetry Theorem for Nonshifted Birkhoffian Systems on Time Scales

The Lie theorem for Birkhoffian systems with time-scale nonshifted variational problems are studied, including free Birkhoffian system, generalized Birkhoffian system and constrained Birkhoffian system. First, the time-scale nonshifted generalized Pfaff-Birkhoff principle is established, and the dynamical equations for three Birkhoffian systems under nonshifted variational problems are deduced. Afterwards, in the time-scale nonshifted variational problems, by introducing the infinitesimal transformations, Lie symmetry for free Birkhoffian system, generalized Birkhoffian system and constrained Birkhoffian system are defined respectively. Then Lie symmetry theorems for three kinds of Birkhoffian systems are deduced and proved. In the end, three examples are given to explain the applications for the results.

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