Open AccessA study on the Lagrangian image of the Birkhoffian representations
Author(s) -
Ding Guang-Tao
Publication year - 2010
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.59.15
Subject(s) - lagrangian , inverse problem for lagrangian mechanics , lagrange multiplier , inverse , order (exchange) , mathematics , image (mathematics) , lagrange polynomial , constraint algorithm , mathematical analysis , computer science , mathematical optimization , mathematical physics , geometry , artificial intelligence , gauge symmetry , finance , gauge theory , polynomial , economics
The Lagrangian image of the Birkhoffian representations is studied. The conditions that the second-order Lagrangians should satisfy are obtained, under which the generalized Lagrange equations are second-order differential equations. A new way for solving the inverse problem in Lagrange mechanics is presented. An error made in the study by some author is pointed out. Two examples are given to illustrate the application of the result.