耗散动力系统的Lie对称性、Jacobi最后乘子和新的非标准Lagrange量
Lie symmetries, Jacobi last multipliers and new non-standard Lagrangians for dissipative dynamical systems
摘要：
我们提出了一种新的方法的基础上李对称性和雅可比最后乘子，它允许一个找到许多非标准拉格朗日耗散动力系统。特别是，它表明，对于每一个非标准拉格朗日可以生成一个新的非标准拉格朗日相关联的一个新的运动方程。我们指出，一个给定的动力系统的Lie对称性的知识产生的Jacobi最后乘子，可以用来获得新的非标准拉格朗日耗散动力系统在一个简单和直接的方式。我们将新方法推广到自由粒子和简谐振子的情形，得到了耗散系统的新的非标准拉格朗日量。
英文摘要：
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.
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