Journal
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
Volume 20, Issue 4, Pages 443-464Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10883-014-9211-1
Keywords
Euler elastica; Optimal control; Exponential mapping
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Funding
- Russian Foundation for Basic Research [12-01-00913-a, 13-01-91162-GFEN-a]
- Russian Federation for the State Support of Researches [14.B25.31.0029]
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The Euler problem on optimal configurations of elastic rod in the plane with fixed endpoints and tangents at the endpoints is considered. The global structure of the exponential mapping that parameterises extremal trajectories is described. It is proved that open domains cut out by the Maxwell strata in the preimage and image of the exponential mapping are mapped diffeomorphically. As a consequence, computation of globally optimal elasticae with given boundary conditions is reduced to solving systems of algebraic equations having unique solutions in the open domains. For certain special boundary conditions, optimal elasticae are presented.
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