TY - JOUR
A2 - Marin, Marin
AU - Guangbao, Wang
AU - Guangtao, Ding
PY - 2020
DA - 2020/08/01
TI - The Lagrangian and Hamiltonian for the Two-Dimensional Mathews-Lakshmanan Oscillator
SP - 2378989
VL - 2020
AB - The purpose of this paper is to illustrate the theory and methods of analytical mechanics that can be effectively applied to the research of some nonlinear nonconservative systems through the case study of two-dimensionally coupled Mathews-Lakshmanan oscillator (abbreviated as M-L oscillator). (1) According to the inverse problem method of Lagrangian mechanics, the Lagrangian and Hamiltonian function in the form of rectangular coordinates of the two-dimensional M-L oscillator is directly constructed from an integral of the two-dimensional M-L oscillators. (2) The Lagrange and Hamiltonian function in the form of polar coordinate was rewritten by using coordinate transformation. (3) By introducing the vector form variables, the two-dimensional M-L oscillator motion differential equation, the first integral, and the Lagrange function are written. Therefore, the two-dimensional M-L oscillator is directly extended to the three-dimensional case, and it is proved that the three-dimensional M-L oscillator can be reduced to the two-dimensional case. (4) The two direct integration methods were provided to solve the two-dimensional M-L oscillator by using polar coordinate Lagrangian and pointed out that the one-dimensional M-L oscillator is a special case of the two-dimensional M-L oscillator.
SN - 1687-9120
UR - https://doi.org/10.1155/2020/2378989
DO - 10.1155/2020/2378989
JF - Advances in Mathematical Physics
PB - Hindawi
KW -
ER -