Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion

Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion

About a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile that is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnier’s work and provided a valid argument for a c...

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Main Authors: Robert Kantrowitz, Michael M. Neumann
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2019/4868106
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spelling doaj-f3f2a918d0524223b96c360d80ffdcf82020-11-25T00:40:29ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252019-01-01201910.1155/2019/48681064868106Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile MotionRobert Kantrowitz0Michael M. Neumann1Mathematics Department, Hamilton College, 198 College Hill Road, Clinton, NY 13323, USADepartment of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USAAbout a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile that is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnier’s work and provided a valid argument for a certain special case. The goal of the present article is to establish a rigorous new approach to the full result. For this, we develop a theory of those functions which can be sandwiched, in a natural way, by a pair of quadratic polynomials. It turns out that the convexity or concavity of the derivative plays a decisive role in this context.http://dx.doi.org/10.1155/2019/4868106
collection DOAJ
language English
format Article
sources DOAJ
author Robert Kantrowitz
Michael M. Neumann
spellingShingle Robert Kantrowitz
Michael M. Neumann
Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion
International Journal of Mathematics and Mathematical Sciences
author_facet Robert Kantrowitz
Michael M. Neumann
author_sort Robert Kantrowitz
title Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion
title_short Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion
title_full Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion
title_fullStr Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion
title_full_unstemmed Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion
title_sort parabolic sandwiches for functions on a compact interval and an application to projectile motion
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2019-01-01
description About a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile that is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnier’s work and provided a valid argument for a certain special case. The goal of the present article is to establish a rigorous new approach to the full result. For this, we develop a theory of those functions which can be sandwiched, in a natural way, by a pair of quadratic polynomials. It turns out that the convexity or concavity of the derivative plays a decisive role in this context.
url http://dx.doi.org/10.1155/2019/4868106
work_keys_str_mv AT robertkantrowitz parabolicsandwichesforfunctionsonacompactintervalandanapplicationtoprojectilemotion
AT michaelmneumann parabolicsandwichesforfunctionsonacompactintervalandanapplicationtoprojectilemotion
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