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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Bibliographic Details
Published in:International journal of mathematics and mathematical sciences 2019, Vol.2019 (2019), p.1-7
Main Authors: Kantrowitz, Robert, Neumann, Michael M.
Format: Article
Language:English
Subjects:
Applied mathematics
Concavity
Convex analysis
Convexity
Mathematical analysis
Mathematical functions
Ordinary differential equations
Polynomials
Projectiles
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Summary: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.
ISSN:0161-1712
1687-0425
DOI:10.1155/2019/4868106