Unified approach to Hamiltonian systems, Poisson systems, gradient systems, and systems with Lyapunov functions or first integrals

被引：71
|
作者：
McLachlan, RI [1 ]
Quispel, GRW
Robidoux, N
机构：
[1] Massey Univ, Dept Math, Palmerston North, New Zealand
[2] La Trobe Univ, Dept Math, Bundoora, Vic 3083, Australia
[3] Massey Univ, Dept Math, Palmerston North, New Zealand
来源：
PHYSICAL REVIEW LETTERS | 1998年 / 81卷 / 12期
关键词：
D O I：
10.1103/PhysRevLett.81.2399
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We show that systems with a first integral (i.e., a constant of motion) or a Lyapunov function can be written as "linear-gradient systems," (x) over dot = L(x)del V(x), for an appropriate matrix function L, with a generalization to several integrals or Lyapunov functions. The discrete-time analog, Delta x/Delta t = L<(del)over bar>V, where V is a "discrete gradient," preserves V as an integral or Lyapunov function, respectively. [S0031-9007(98)07076-8].
引用
收藏
页码：2399 / 2403
页数：5
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