We derived a condition under which a coupled system consisting of two finite-dimensional Hamiltonian systems becomes a Hamiltonian system. In many cases, an industrial system can be modeled as a coupled system of some subsystems. Although it is known that symplectic integrators are suitable for discretizing Hamiltonian systems,the composition of Hamiltonian systems may not be Hamiltonian. In this paper, focusing on a property of Hamiltonian systems, that is, the conservation of the symplectic form, we provide a condition under which two Hamiltonian systems coupled with interactions compose a Hamiltonian system.
翻译:我们得出一个条件,即由两种有限维度的汉密尔顿系统构成的结合系统成为汉密尔顿系统,在许多情况下,工业系统可以作为某些子系统的结合系统进行模拟,尽管已知交替融合器适合分离汉密尔顿系统,但汉密尔顿系统的组成可能不是汉密尔顿系统,在本文件中,侧重于汉密尔顿系统的一个属性,即保护中间形式,我们提供了一个条件,使两个汉密尔顿系统加上相互作用组成汉密尔顿系统。