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

Abstract EN

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.