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

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  • Robert Kantrowitz
  • Michael M. Neumann

Abstract

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.

Suggested Citation

  • Robert Kantrowitz & Michael M. Neumann, 2019. "Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2019, pages 1-7, May.
    • Handle: RePEc:hin:jijmms:4868106
    DOI: 10.1155/2019/4868106
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