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On Optimum Propulsion by Means of Small Periodic Motions of a Rigid Profile. I. Properties of Optimum Motions
Author(s) -
Urbach H. P.
Publication year - 1990
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1990822121
Subject(s) - inviscid flow , lagrange multiplier , thrust , mathematics , compressibility , constraint algorithm , amplitude , constraint (computer aided design) , mathematical analysis , multiplier (economics) , classical mechanics , geometry , physics , mathematical optimization , mechanics , macroeconomics , quantum mechanics , economics , thermodynamics
The problem of optimum thrust generation by means of a rigid profile performing small arbitrarily periodic motions in an inviscid incompressible fluid is studied. The motions considered have to generate a prescribed mean value of thrust and must be such that the contribution to this mean thrust by the suction at the leading edge does not exceed a certain given value. Furthermore, the motions are in general subjected to a maximum type constraint on their amplitude. For this infinite dimensional, nonconvex and nonsmooth optimization problem, a generalized Lagrange multiplier rule is derived. In case the constraint on the amplitude is omitted, the optimum motions are calculated analytically; for the general case a number of properties of the solutions are derived from the Lagrange multiplier rule.