论文标题
无效的拉格朗日人在动态系统运动方程方程的推导中的新作用
New Role of Null Lagrangians in Derivation of Equations of Motion for Dynamical Systems
论文作者
论文摘要
无效拉格朗日人的空间是动态研究最少的领域，因为它们的欧拉 - 拉格朗日操作员将它们相同地发送至零，从而对运动方程没有影响。通过引入广泛的程序（就本文作者的最新程序而言，可以利用这些Lagrangians的无效性来构建代表一系列有趣的动态系统的非标准的Lagrangians，这是通过引入广泛的程序（就本文作者的最新程序而进行的）来发现这些无效的动态中的相关性的谦虚努力。通过使用广义过程，介绍了谐波振荡器以及Bateman和Duffing振荡器的运动方程式的推导。获得的结果表明，无效的Lagrangians及其相应的非标准Lagrangians在描述线性和非线性以及耗散性和非疾病动力学系统中扮演的新作用。
The space of Null Lagrangians is the least investigated territory in dynamics since they are identically sent to zero by their Euler-Lagrange operator and thereby having no effects on equations of motion. A humble effort to discover the relevance of these Null Lagrangians in dynamics is made by introducing a generalized procedure (with respect to the recent procedure introduced by the authors of this paper) that takes advantage of the null-ness of these Lagrangians to construct non-standard Lagrangians that represent a range of interesting dynamical systems. By using the generalized procedure, derivation of equations of motion for a harmonic oscillator as well as for the Bateman and Duffing oscillators is presented. The obtained results demonstrate a new role played by the null Lagrangians and their corresponding non-standard Lagrangians in describing linear and nonlinear, and dissipative and non-dissipative dynamical systems.
