In an attempt to generalize Hamilton's principle, an action functional is proposed which, unlike the standard version of the principle, accounts properly for all initial data and the possible presence of dissipation. To this end, the convolution is used instead of the L² inner product so as to eliminate the undesirable end temporal condition of Hamilton's principle. Also, fractional derivatives are used to account for dissipation and the Dirac delta function is exploited so as the initial velocity can be inherently set into the variational setting. The proposed approach applies to both finite- and infinite-dimensional systems.

中文翻译：

---

关于离散和连续系统的汉密尔顿原理：卷积作用原理

为了概括汉密尔顿原理，提出了一种动作功能，与该原理的标准版本不同，该功能适当地考虑了所有初始数据以及可能存在的耗散。为此，使用卷积代替L ²内积，以消除汉密尔顿原理的不希望的最终时间条件。同样，分数导数用于解释耗散，并且利用Dirac delta函数，以便可以将初始速度固有地设置为变分设置。所提出的方法适用于有限维和无限维系统。