Extensions of Noether's Second Theorem: from continuous to discrete systems
Extensions of Noether's Second Theorem: from continuous to discrete systems
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DOI：
10.1098/rspa.2011.0158
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发表时间：
2011-03
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影响因子：
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通讯作者：
P. Hydon;E. Mansfield
中科院分区：
文献类型：
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作者：
P. Hydon;E. Mansfield
给出了诺特第二定理的一个简单的局部证明。这个证明立即导致定理的推广，得到守恒定律和/或任何变分问题的欧拉-拉格朗日方程之间的显式关系，这些变分问题的对称性取决于一组自由或部分约束的函数。我们的方法进一步扩展到处理有限差分系统。结果很容易应用；用几个著名的连续系统和离散系统作为例子。
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler–Lagrange equations of any variational problem whose symmetries depend on a set of free or partly constrained functions. Our approach extends further to deal with finite-difference systems. The results are easy to apply; several well-known continuous and discrete systems are used as illustrations.