A nonholonomic approach to isoparallel problems and some applications

Autor:	Hernán Cendra, Sebastián J. Ferraro
Rok vydání:	2006
Předmět:	Geodesic Parallel transport General Mathematics Fundamental theorem of Riemannian geometry Levi-Civita connection Frame bundle Computer Science Applications Intrinsic metric Algebra symbols.namesake symbols Fisher information metric Metric connection Mathematics
Zdroj:	Dynamical Systems. 21:409-437
ISSN:	1468-9375 1468-9367
DOI:	10.1080/14689360600734112
Popis:	Isoparallel problems are a class of optimal control problems on principal fibre bundles endowed with a connection and a Riemannian metric on the base space. These problems consist of finding the shortest curve on the base among those with a given parallel transport operator. It has been shown that when the structure group of the principal bundle admits a bi-invariant metric, the normal solutions are precisely the projections of the geodesics (relative to an appropriate Riemannian metric) on the bundle. In this work we obtain a generalization of this result that holds true for any structure group, by transforming the isoparallel problem into a nonholonomic problem of a generalized type. The latter reduces to the geodesic problem if the structure group has a bi-invariant metric. We illustrate the theory with an application to the optimal control of an elastic rolling ball (the plate–ball system), relating some aspects of this problem to the dynamics of a simple pendulum. Finally, we indicate how the study o...
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::654e9c6cadd9499b2191abdee07062f1 https://doi.org/10.1080/14689360600734112 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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