论文标题
非标准的null lagrangians和仪表功能和动力学中的耗散力
Nonstandard Null Lagrangians and Gauge Functions and Dissipative Forces in Dynamics
论文作者
论文摘要
给出相同运动方程式的标准和非标准的拉格朗日在其形式上有显着差异，因为后者没有明显可见的能量样表达式的术语。这些Lagrangians的特殊家庭是无效的Lagrangians及其仪表功能。结果表明，非标准的null Lagrangians及其规格函数可用于将耗散力引入动力系统。随着标准的null Lagrangians以引入非隔离力而闻名，提出的结果可以完整地了解Null Lagrangians在将力引入动力学中扮演的新角色。提出了结果对牛顿法律的应用，并讨论了其伽利略的不变性。
Standard and non-standard Lagrangians that give the same equation of motion are significantly different in their forms, as the latter do not have terms that clearly discernable energy-like expressions. A special family of these Lagrangians are null Lagrangians and their gauge functions. It is shown that non-standard null Lagrangians and their gauge functions can be used to introduce dissipative forces to dynamical systems. With standard null Lagrangians being known for introducing non-dissipative forces, the presented results allow for a complete picture of novel roles played by null Lagrangians in introducing forces to dynamics. Applications of the results to Newton's laws are presented and their Galilean invariance is discussed.
