论文标题
Herglotz耗散田地理论的变分原理
The Herglotz variational principle for dissipative field theories
论文作者
论文摘要
近年来，随着接触几何形状的结合，人们对在物理和其他应用数学领域的耗散或非保守系统的研究引起了人们的兴趣。研究接触时产生的方程式也可以通过Herglotz变化原理获得。机械系统的拉格朗日和哈密顿形式主义的联系也已被推广到现场理论。本文的主要目的是为一阶和高阶现场理论开发Herglotz变异原理的概括。为了说明这一点，我们研究了三个例子：阻尼的振动字符串，Korteweg-de Vries方程，以及一个学术示例，表明非全面的变异原理并不完全等效。
In the recent years, with the incorporation of contact geometry, there has been a renewed interest in the study of dissipative or non-conservative systems in physics and other areas of applied mathematics. The equations arising when studying contact Hamiltonian systems can also be obtained via the Herglotz variational principle. The contact Lagrangian and Hamiltonian formalisms for mechanical systems has also been generalized to field theories. The main goal of this paper is to develop a generalization of the Herglotz variational principle for first-order and higher-order field theories. In order to illustrate this, we study three examples: the damped vibrating string, the Korteweg-De Vries equation, and an academic example showing that the non-holonomic and the vakonomic variational principles are not fully equivalent.
