Applied Mathematics and Mechanics

, Volume 16, Issue 4, pp 301–306 | Cite as

The Hamiltonian structures of 3D ODE with time-independent invariants

  • Guo Zhong-heng
  • Chen Yu-ming


We have proved that any 3-dimensional dynamical system of ordinary differential equations (in short, 3D ODE) with time-independent invariants can be rewritten as Hamiltonian systems with respect to generalized Poisson brackets and the Hamiltonians are these invariants. As an example, we discuss the Kermack-Mckendrick model for epidemics in detail. The results we obtained are generalization of those obtained by Y. Nutku.

Key words

Poisson bracket Hamiltonian structure bi-Hamiltonian structure invariant the Kermack-Mckendrick model for epidemics 


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Copyright information

© Shanghai University of Technology (SUT) 1995

Authors and Affiliations

  • Guo Zhong-heng
    • 1
  • Chen Yu-ming
    • 2
  1. 1.Department of MathematicsPeking UniversityBeijingP. R. China
  2. 2.Department of Applied MathematicsHuman UniversityChangshaP. R. China

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