A sructure‐preserving numerical method for the dynamic optimization of flexible mechanical systems. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Schneider, Simeon; Betsch, Peter
• 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.201800286
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: If an optimal control problem has symmetries, associated generalized momentum maps are preserved quantities along an optimal path, as can be seen by the extension of Noether's theorem to optimal control problems. These symmetries on the control level are inherited from the underlying mechanical system. The presented discretization method does respect the symmetries on both levels, the mechanical system and the optimal control problem, and preserves the generalized momentum mapping.