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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 1, Pages 87–100
(Mi smj1824)
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This article is cited in 5 scientific papers (total in 5 papers)
Generalized distance functions of Riemannian manifolds and the motions of gyroscopic systems
Yu. V. Ershov, E. I. Yakovlev N. I. Lobachevski State University of Nizhni Novgorod
Abstract:
We use the homology groups of the path space of an arbitrary Riemannian manifold to define some analogs of the distance function and study their main properties. For the natural systems with gyroscopic forces we prove an existence theorem for solutions to the two-point boundary value problem, which complements the results of [1]. We apply the geodesic modeling method of [1], [2], using the generalized distance functions.
Keywords:
Riemannian manifold, path space, generalized distance function, gyroscopic system, many-valued functional, extremal.
Received: 25.10.2006
Citation:
Yu. V. Ershov, E. I. Yakovlev, “Generalized distance functions of Riemannian manifolds and the motions of gyroscopic systems”, Sibirsk. Mat. Zh., 49:1 (2008), 87–100; Siberian Math. J., 49:2 (2008), 69–79
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https://www.mathnet.ru/eng/smj1824 https://www.mathnet.ru/eng/smj/v49/i1/p87
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Abstract page: | 374 | Full-text PDF : | 92 | References: | 51 | First page: | 4 |
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