论文标题
汉密尔顿 - 雅各比理论和自主和非自主接触系统的可集成性
Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
论文作者
论文摘要
在本文中，我们研究了接触式哈密顿系统的整合性，包括时间依赖性和独立。为了这样做，我们构建了汉密尔顿 - 雅各比理论，以遵循两种方法，获得了两种不同的汉密尔顿 - 雅各比方程。与保守的哈密顿系统相比，接触式哈密顿系统取决于一个附加参数。获得两个方程式的事实反映了我们是否正在根据此附加参数寻找解决方案。为了说明本文开发的理论，我们研究了三个示例：具有线性外力的自由粒子，带有线性耗散的自由掉落粒子以及阻尼和强制的谐波振荡器。
In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton--Jacobi theory for these systems following two approaches, obtaining two different Hamilton--Jacobi equations. Compared to conservative Hamiltonian systems, contact Hamiltonian systems depend of one additional parameter. The fact of obtaining two equations reflects whether we are looking for solutions depending on this additional parameter or not. In order to illustrate the theory developed in this paper, we study three examples: the free particle with a linear external force, the freely falling particle with linear dissipation and the damped and forced harmonic oscillator.
