Journal of University of Science and Technology of China ›› 2018, Vol. 48 ›› Issue (8): 643-648.DOI: 10.3969/j.issn.0253-2778.2018.08.007

• Original Paper • Previous Articles     Next Articles

Poisson bracket method for obtaining normal coordinates of quadratic Hamiltonian

  

  1. LIN Quan, FAN Hongyi2
  • Received:2018-03-29 Revised:2018-05-25 Accepted:2018-05-25 Online:2018-08-31 Published:2018-05-25
  • Contact: LIN Quan
  • About author:LIN Quan (corresponding author), male, born in 1980, master/ associate Prof. Research field:Theoretical mechanics and mechanical design .E-mail: 12959392@qq.com
  • Supported by:
    Supported by the National Natural Science Foundation of China (11775208), Education and Sci-Tech Projects for Young and Middle-aged Teachers in Fujian Province (JK2014053), Educational Research Projects for Young and Middle-aged Teachers in Fujian Province (JAT170582).

Abstract: It was found that the problem of searching for normal coordinates W of quadratic Hamiltonian H can be ascribed to solving the newly established secular equation with two consecutive Poisson bracket operations. Solving W would simultaneously lead to the normal frequency. Some examples about quadratic Hamiltonian were presented to demonstrate the effectiveness of the presented method.

Key words: quadratic Hamiltonian, Poisson bracket operations, normal coordinates, normal frequency

CLC Number: