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More on the Problem and the Solution of the Optimal Shape of a Javelin
Author(s) -
Atanacković Teodor M.,
Bačlić Branislav S.
Publication year - 2007
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 - 10.1111/j.1467-9590.2006.00382.x
Subject(s) - javelin , mathematics , a priori and a posteriori , mathematical analysis , geometry , mathematical optimization , classical mechanics , physics , throwing , philosophy , epistemology
The analogy between the optimal javelin problem and the problem of determining the optimal shape of the free rotating rod has been established and employed to determine the optimal shape of the javelin via Pontryagin's maximum principle. Five distinct variational principles are constructed for boundary value problem describing optimal shape of the javelin. The first integral for this nonlinear system is found. An a priori estimate of the cross‐sectional area is obtained. The optimal shape of the javelin or free rotating rod is determined by numerical integration.