Halley’s minimal kinetic energy problem for projectile motion with drag quadratic in speed
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In papers published in the Philosophical Transactions in the late 1600s, Edmond Halley highlighted the problem of delivering a projectile to its intended target with minimal kinetic energy upon impact. Halley accounted for the force of gravity acting on the projectile, but ignored the retarding effect of air resistance. In this article, we revive the optimization problem raised by Halley, here allowing for drag that is quadratic in speed. It turns out that there are remarkable parallels between the optimal flight curve in the case of no air resistance and that in which air resistance is quadratic in speed.
KeywordsProjectile ballistics Linear drag Quadratic drag Halley’s minimal kinetic energy problem
Mathematics Subject ClassificationPrimary 26A06 Secondary 49K15
We thank the referees for their careful reading and valuable suggestions.
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