ABSTRACT

In the present work we obtain the constants of motion for isoperimetric variational problems with time delay. We consider a constrained optimization problem where the Lagrangian function defining the functional depends on time delayed arguments. We prove the isoperimetric Euler–Lagrange and DuBois–Reymond type optimality conditions and, in order to investigate the constants of motion for this problem, we obtain a nonsmooth extension of Noether's symmetry theorem for isoperimetric variational problems with delayed arguments.

中文翻译：

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具有时间延迟的等周变分问题的运动常数

摘要

在目前的工作中，我们获得了具有时间延迟的等周变分问题的运动常数。我们考虑一个约束优化问题，其中定义函数的拉格朗日函数取决于时间延迟的参数。我们证明了等周 Euler-Lagrange 和 DuBois-Reymond 型最优性条件，并且为了研究该问题的运动常数，我们获得了 Noether 对称定理的非光滑扩展，用于具有延迟参数的等周变分问题。