论文标题
谎言对称性，雅各比的最后乘数和新的非标准拉格朗日用于散发性动力学系统
Lie symmetries, Jacobi last multipliers and new non-standard Lagrangians for dissipative dynamical systems
论文作者
论文摘要
我们提出了一种基于谎言对称性和雅各比的新方法，该方法使人们可以找到许多非标准的Lagrangians用于耗散动力学系统。特别是，对于每个非标准的拉格朗日人都可以生成与新运动方程相关的新的非标准拉格朗日。我们指出，给定动力学系统的Lie对称性知识生成了Jacobi的最后乘数，可用于以简单明了的方式获得新的非标准的Lagrangians用于耗散动力学系统。我们通过将其应用于自由粒子和简单的谐波振荡器的情况来体现新方法，以便为耗散系统获得新的非标准lagrangians。
We present a new method based on Lie symmetries and Jacobi last multipliers which allows one to find many non-standard Lagrangians for dissipative dynamical systems. In particular, it is demonstrated that for every non-standard Lagrangian one can generate a new non-standard Lagrangian associated to a new equation of motion. We point out that the knowledge of Lie symmetries for a given dynamical system generates Jacobi last multipliers which can be used to obtain new non-standard Lagrangians for dissipative dynamical systems in a simple and straightforward way. We exemplify the new method by applying it to the case of the free particle and the simple harmonic oscillator in order to obtain new non-standard Lagrangians for dissipative systems.
