Differential invariants of a class of Lagrangian systems with two degrees of freedom

被引：4

作者：

Bagderina, Yulia Yu. ^{[1
]}

Tarkhanov, Nikolai N. ^{[2
]}

机构：

[1] Russian Acad Sci, Ctr Comp, Inst Math, Ufa 450008, Russia

[2] Univ Potsdam, Inst Math, D-14469 Potsdam, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 410卷 / 02期

关键词：

Equivalence; Differential invariant; Euler-Lagrange equations; HIGHER-ORDER LAGRANGIANS; EQUIVALENCE PROBLEM; SYMMETRIES; CLASSIFICATION;

D O I：

10.1016/j.jmaa.2013.08.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：733 / 749

页数：17

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