标题： 时间依赖耗散力学系统的拉格朗日-哈密顿形式主义 显示英文标题

标题： Lagrangian-Hamiltonian formalism for time-dependent dissipative mechanical systems

摘要： 在本文中，我们提出了一种统一的拉格朗日-哈密顿几何形式，用于描述时间依赖的接触力学系统，该方法基于K. Kamimura首先引入的理论，后来由R. Skinner和R. Rusk进行了形式化。 当处理由奇异拉格朗日量描述的系统时，这种形式尤其有趣，因为二阶条件是从约束算法中恢复的。 为了说明这一形式，详细描述了一些相关示例：杜芬方程、具有时间依赖质量与二次阻力的上升粒子，以及在静态电场中具有时间依赖约束的带电粒子。 显示英文摘要

摘要： In this paper we present a unified Lagrangian--Hamiltonian geometric formalism to describe time-dependent contact mechanical systems, based on the one first introduced by K. Kamimura and later formalized by R. Skinner and R. Rusk. This formalism is especially interesting when dealing with systems described by singular Lagrangians, since the second-order condition is recovered from the constraint algorithm. In order to illustrate this formulation, some relevant examples are described in full detail: the Duffing equation, an ascending particle with time-dependent mass and quadratic drag, and a charged particle in a stationary electric field with a time-dependent constraint.