一种构造可积Hamilton系统的新方法
A New Method for the Construction of Integrable Hamiltonian Systems
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摘要: 建议了一种新的构造可积Hamilton系统的方法。对于给定的Poisson流形,本文利用Dirac-Poisson结构构造其上的新Poisson括号[1],进而获得了新的可积Hamilton系统。构造的Poisson括号一般是非线的,并且这种方法也不同于通常的方法[2～4]。本文还给出了两个实例。
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关键词:
- Dirac－Poisson括号 /
- 可积性 /
- Hamilton系统
Abstract: A new method for the construction of integrable Hamiltonian system is proposed.For a given Poisson manifold the present paper constructs new Poisson brackets on it by making use of the Dirac-Poisson structure([1]),and obtains, further new integrable Hamiltonian systems. The constructed Poisson bracket is usual non-linear, and this new method is also different from usual ones([2-4]).Two examples are given.-
Key words:
- Dirac-Poisson bracket /
- integrability /
- Hamiltonian systems
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[1] P.A.M.Dirac,Generalized Hamilton dynamics,Can.J.Math.,2(1950),129-148. [2] V.I.Arnold,et al.(eds),Dynamical Systems(VI),Springer-Verlag (1992),116-220. [3] B.Kostant,Adv.Math.,34(1979),195. [4] R.Abraham and J.Marsden,Forardations of Mechanics,2nd ed,Addison-Wesley,Reading,Mass(1978),298-304. [5] D.H.Sattinger and O.L.Weaver,Lie Groups and Algebra with Applications to Plorsics.Geometry and Mechanics,Springer-Verlag(1986). [6] L.D.Faddeev and L.A.Takhtajan,Hamihonian Methods in the Theory of Solutions,Springer-Verlag(1987). -
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