Geometric calculus for second-order differential equations and generalizations of the inverse problem of Lagrangian mechanics

被引：5

作者：

Sarlet, W. ^{[1
,2
]}

机构：

[1] Univ Ghent, Dept Math, B-9000 Ghent, Belgium

[2] La Trobe Univ, Dept Math & Stat, Bundoora, Vic 3086, Australia

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2012年 / 47卷 / 10期

关键词：

Tangent bundle geometry; Second-order differential equations; Lagrangian systems; Inverse problem; QUASI-TANGENT STRUCTURE; HELMHOLTZ CONDITIONS; BERWALD-TYPE; CONNECTIONS; DERIVATIONS; SYSTEMS; FORMS;

D O I：

10.1016/j.ijnonlinmec.2011.09.005

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We review the main features of the geometric calculus which has been introduced over the past 15 years in the study of second-order ordinary differential equations and then explain how a recently introduced generalization of the inverse problem of Lagrangian mechanics can be very concisely dealt with by this calculus in an intrinsic way. This paper is an account of the lecture with the same title presented at the ICDVC-2010 Conference in Hangzhou, May 12-14 (2010). (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1132 / 1140

页数：9

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