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Maxwell strata in Euler's elastic problem

Show simple item record Sachkov, Yuri L. en_US 2007-03-02T12:19:39Z en_US 2011-09-07T20:27:01Z 2007-03-02T12:19:39Z en_US 2011-09-07T20:27:01Z 2007-03-02T12:19:39Z en_US
dc.identifier.uri en_US
dc.description.abstract The classical Euler's problem on stationary configurations of elastic rod with fixed endpoints and tangents at the endpoints is considered as a left-invariant optimal control problem on the group of motions of a twodimensional plane E(2). The attainable set is described, existence and boundedness of optimal controls are proved. Extremals are parametrized by Jacobi's elliptic functions of natural coordinates induced by the flow of the mathematical pendulum on fibers of the cotangent bundle of E(2). The group of discrete symmetries of Euler's problem generated by reflections in the phase space of the pendulum is studied. The corresponding Maxwell points are completely described via the study of fixed points of this group. As a consequence, an upper bound on cut points in Euler's problem is obtained. en_US
dc.format.extent 1872630 bytes en_US
dc.format.mimetype application/pdf en_US
dc.language.iso en_US en_US
dc.relation.ispartofseries SISSA;04/2007/M en_US
dc.relation.ispartofseries;0705.0614v1 en_US
dc.title Maxwell strata in Euler's elastic problem en_US
dc.type Preprint en_US
dc.contributor.department Functional Analysis and Applications en_US
dc.contributor.area Mathematics en_US

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