On different geometric approaches to the dynamics of finite‐dimensional mechanical systems. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Eugster, Simon R.; Capobianco, Giuseppe; Winandy, Tom
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900327
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: The language of differential geometry allows a coordinate‐free representation of physical quantities. This led to the development of several geometric theories for the description of finite‐dimensional mechanical systems. These approaches differ in the mathematical concepts they invoke and in the classes of mechanical systems they can describe. This short note aims to give an overview on the following three popular approaches, all of which are limited to time‐independent mechanical systems. While in the first approach, the motion of the mechanical system is considered as a curve in the system's configuration manifold, in the latter two, the corresponding motions are interpreted as curves in the tangent or the cotangent bundle of the configuration manifold.