标题： 基于虚功泛函的诺特定理的推广 显示英文标题

标题： A generalization of Noether's theorem based on the virtual work functional

摘要： 在作者之前的一系列文章中，已经表明可以通过从虚功泛函而不是作用泛函开始，有效地为非保守力学系统以及受非完整约束的系统提供变分公式。 在本文中，当从一个不精确的虚功泛函开始时，即它不承认一个作用泛函时，Noether定理的扩展给出了非守恒电流的平衡原理，而不是守恒定律。 给出了这种广义Noether恒等式的例子，涉及质点、刚体和可变形体的力学。 显示英文摘要

摘要： In a series of previous articles by the author, it was shown that one could effectively give a variational formulation to non-conservative mechanical systems, as well as ones that subject to non-holonomic constraints by starting with the virtual work functional instead of an action functional. In this article, it is shown that when one starts with a virtual work functional that is not exact, so it does not admit an action functional, instead of conservation laws the extension of Noether's theorem gives balance principles for non-conserved currents. Examples of this generalized Noether identity are given in the mechanics of points, rigid bodies, and deformable bodies.