论文标题
动态系统的Noether Bessel Hagen对称方法
The Noether Bessel Hagen Symmetry Approach for Dynamical Systems
论文作者
论文摘要
Noether-Bessel-Hagen定理可以被认为是Noether定理以搜索对称性的自然扩展。在这里，我们开发了介绍该方法基本基础的动力系统的方法。具体而言，我们建立了存在外力的机械系统的Noether-Bessel-Hagen分析。在本文的第二部分中，采用该方法来选择给定系统的对称性。特别是，我们将重点放在谐波振荡器作为该理论的测试床上，以及来自标量调节引力的宇宙学系统，具有标量的标量势势$ V（φ）$。我们表明，通过对称的存在选择电势的形状。当给定系统的拉格朗日人无法立即识别或不是拉格朗日系统后，该方法结果特别有用。
The Noether-Bessel-Hagen theorem can be considered a natural extension of Noether Theorem to search for symmetries. Here, we develop the approach for dynamical systems introducing the basic foundations of the method. Specifically, we establish the Noether-Bessel-Hagen analysis of mechanical systems where external forces are present. In the second part of the paper, the approach is adopted to select symmetries for a given systems. In particular, we focus on the case of harmonic oscillator as a testbed for the theory, and on a cosmological system derived from scalar-tensor gravity with unknown scalar-field potential $V (φ)$. We show that the shape of potential is selected by the presence of symmetries. The approach results particularly useful as soon as the Lagrangian of a given system is not immediately identifiable or it is not a Lagrangian system.
