Open AccessThe discussion on Lagrange equation containing third order derivatives
Author(s) -
Shengli Ma,
Xue-Xiang Xu,
Huang Pei-Tian,
Li-Yun Hu
Publication year - 2004
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.53.3648
Subject(s) - constraint algorithm , third order , lagrange multiplier , equations of motion , order (exchange) , motion (physics) , euler–lagrange equation , integro differential equation , mathematical analysis , mathematics , physics , riccati equation , classical mechanics , differential equation , lagrangian , mathematical optimization , finance , economics , philosophy , theology
In this paper, the third order Lagrange equation is obtained, by which can be obtained motion equation of a body. This equation contains third order rate of change of generalized coordinates and the rate of change of force. In addition, the third order Lagrange equation and the fraditional Lagrange equation are used to solve the same problem of the motion of a body, and their results are discussed. Finally, it is pointed out that the third order Lagrange equation provides a method of obtaining equation of motion which is different from that of the traditional Lagrange equation.