Variational calculation and symplectic structure of Hamiltonian systems based the discrete Legenda transformations
XIA Lili1,2， GUO Zhongjin1,3， ZHANG Wei1
1.College of Mechaniacl Engineering， Beijing University of Technology， Beijing 100124；2. College of Physical and Eelectronic Engineering， Henan Institute of Education， Zhengzhou 450046；3.School of Mathematics and Statistics， Taishan University， Taian， Shandong 271000
Abstract：Three types of discrete Legenda transformations are obtained when the displacement coordinates are defined implicitly by different momentum. The different forms of Hamiltonian equations are constructed based on the difference Legenda transformations. The symplectic structures of the three Hamilton systems are given， respectively. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show the advantage of variational numerical method.
夏丽莉,国忠金,张 伟. 基于离散Legenda变换的Hamilton系统的变分算法和辛结构[J]. 华中师范大学学报(自然科学版), 2017, 51(4): 449-454.
XIA Lili,GUO Zhongjin,ZHANG Wei. Variational calculation and symplectic structure of Hamiltonian systems based the discrete Legenda transformations. journal1, 2017, 51(4): 449-454.
2017, Vol. 51 
