论文标题
无效的Lagrangians和量规功能在动态系统中的功能：力和非线性
Null Lagrangians and Gauge Functions in Dynamical Systems: Forces and Nonlinearities
论文作者
论文摘要
在不同的Lagrangians中，Null Lagrangians以相同的Euler-Lagrange方程为零而闻名，因此，它们对最终的运动方程没有影响。但是，有一个特殊的无效拉格朗日家族，可用于将线性和未发动的运动方程式转换为非线性和驱动的运动。为了确定这个特殊的家族，为二阶运动的二阶运动方程式构建了一般的零lagrangians及其规格函数，描述了一维动力学系统。介绍了与力相对应的量规函数，并提出了各种已知动力学系统中的非线性，并讨论了这些功能在动力学中的新作用。
Among different Lagrangians, null Lagrangians are known for having identically zero the Euler-Lagrange equation and, therefore, they have no effects on the resulting equations of motion. However, there is a special family of null Lagrangians that can be used to convert linear and undriven equations of motion into nonlinear and driven ones. To identify this special family, general null Lagrangians and their gauge functions are constructed for second-order ordinary differential equations of motion describing one-dimensional dynamical systems. The gauge functions corresponding to forces and nonlinearities in a variety of known dynamical systems are presented and novel roles of these functions in dynamics are discussed.
