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Note on the existence and uniqueness of optimum lifting surfaces with reduced tip vorticity
Author(s) -
Sparenberg J. A.,
Thomas E. G. F.
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.311
Subject(s) - mathematics , uniqueness , vorticity , bounded function , gravitational singularity , mathematical analysis , action (physics) , square (algebra) , square root , geometry , vortex , mechanics , physics , quantum mechanics
In linearized optimization theory, lifting surfaces shed tip vorticity of which the strength has in general infinite square root singularities. Here we impose, besides the usual condition on the force action of the lifting surfaces, also a condition on the strength of their shed vorticity by which it remains bounded. Then the existence of a unique optimum under both conditions is proved. Copyright © 2002 John Wiley & Sons, Ltd.