论文标题
Lagrangian-Hamiltonian形式主义，用于时期的耗散机械系统
Lagrangian-Hamiltonian formalism for time-dependent dissipative mechanical systems
论文作者
论文摘要
在本文中，我们提出了一个统一的拉格朗日式 - 哈米尔顿几何形式主义，以描述K. Kamimura首次引入的时间依赖性接触机械系统，后来由R. Skinner和R. Rusk正式正式化。在处理奇异拉格朗日描述的系统时，这种形式主义特别有趣，因为从约束算法中恢复了二阶条件。为了说明这种公式，全面描述了一些相关的示例：行驶方程，带有时间依赖的质量和二次阻力的上升粒子，以及具有时间依赖性约束的固定电场中的带电粒子。
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.
