Reference : Submersions, Hamiltonian systems and optimal solutions to the rolling manifolds problem
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/20060
 Title : Submersions, Hamiltonian systems and optimal solutions to the rolling manifolds problem Language : English Author, co-author : Grong, Erlend [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Publication date : 2016 Journal title : SIAM Journal on Control & Optimization Publisher : Society for Industrial & Applied Mathematics Volume : 54 Issue/season : 2 Pages : 536-566 Peer reviewed : Yes (verified by ORBilu) Audience : International ISSN : 0363-0129 e-ISSN : 1095-7138 Keywords : [en] Submersions ; Hamiltonian systems ; Rolling manifolds Abstract : [en] Given a submersion $\pi:Q \to M$ with an Ehresmann connection~$\calH$, we describe how to solve Hamiltonian systems on $M$ by lifting our problem to $Q$. Furthermore, we show that all solutions of these lifted Hamiltonian systems can be described using the original Hamiltonian vector field on $M$ along with a generalization of the magnetic force. This generalized force is described using the curvature of $\calH$ along with a new form of parallel transport of covectors vanishing on $\calH$. Using the Pontryagin Maximum Principle, we apply this theory to optimal control problems $M$ and $Q$ to get results on normal and abnormal extremals. We give a demonstration of our theory by considering the optimal control problem of one Riemannian manifold rolling on another without twisting or slipping along curves of minimal length. Funders : Fonds National de la Recherche - FnR Target : Researchers Permalink : http://hdl.handle.net/10993/20060 DOI : 10.1137/15M1008919 Other URL : http://epubs.siam.org/doi/10.1137/15M1008919 FnR project : FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014

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