A geometric view on the kinematics of finite‐dimensional mechanical systems. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Winandy, Tom; Capobianco, Giuseppe; Eugster, Simon R.
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800221
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Finite‐dimensional mechanical systems can be described in terms of a set of generalized coordinates and their time‐derivatives. In this case, the Lagrange equations of the second kind provide the equations of motion of these systems. The Volterra–Hamel–Boltzmann equations generalize the Lagrange equations of the second kind in the sense that they allow for more general velocity parametrizations. In this work, we show in the context of scleronomous finite‐dimensional mechanical systems that both sets of equations can be interpreted as being different chart representations of the intrinsic Euler–Lagrange equations on the tangent bundle over the configuration manifold of the mechanical system.