Abstract
The aim of this chapter is to offer a short account of classical and recent results about Newton’s problem of minimal resistance available to undergraduate students. Part of this material was presented by the first author in a lecture addressed to undergraduate students of engineering. We begin with a derivation of Newton’s model for the resistance of a body moving with constant velocity in a rare medium. Then we show how to recover from Newton’s geometric constructions, the corresponding solutions to Newton’s aerodynamic problem for the frustum of a cone and for radially symmetric solids. Finally, we consider Newton’s problem for nonsymmetric solids and describe the existence and lack of uniqueness of non-radially symmetric solutions to this minimization question.
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References
Butazzo G, Ferone V, Kawohl B (1995) Minimum problems over sets of concave functions and related questions. Math Nachr 173:71–89
Butazzo G, Ferone V, Kawohl B (1996) A symmetry problem in the calculus of variations. Calc Var 4:593–599
Butazzo G, Kawohl B (2001) On Newton’s problem of minimal resistance. Springer, Heidelberg
Cruz-Sampedro J, Tetlalmatzi-Montiel M (2010) POEM’s and Newton’s aerodynamic frustum. Coll Math J 41(2):145–153
Goldstine H (1980) A history of the calculus of variations. Springer, New York
Marcellini (1989) P Non-convex Integrals of the Calculus of Variations. In: Cellina A (ed) Proceedings of methods of non-convex analysis, Varenna, Lecture notes in mathematics No. 1446. Springer Verlag 1990:16–57
Miele A (1965) Theory of optimum aerodynamic shapes. Academic Press, New York
Newton I (1934) Philosophia naturalis principia mathematica. University of California Press, California (Motte’s Translation)
Tikhomirov VM (1990) Stories about maxima and minima. In: Proceeding of AMS-MAA, Washington
Acknowledgments
Both authors thank the referee for his useful comments and remarks. The first author acknowledges Professor Abraham Medina-Ovando for his kind invitation to participate in the XIX Enzo Levi Seminar, held at Universidad Autónoma Metropolitana Azcapotzalco in Mexico City in the Spring of 2012.
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Cruz-Sampedro, J., Tetlalmatzi-Montiel, M. (2014). Minimum Resistance in a Rare Medium. In: Klapp, J., Medina, A. (eds) Experimental and Computational Fluid Mechanics. Environmental Science and Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-00116-6_9
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DOI: https://doi.org/10.1007/978-3-319-00116-6_9
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