An analytic approach to projectile motion in a linear resisting medium

Seán M. Stewart

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

The time of flight, range and the angle which maximizes the range of a projectile in a linear resisting medium are expressed in analytic form in terms of the recently defined Lambert W function. From the closed-form solutions a number of results characteristic to the motion of the projectile in a linear resisting medium are analytically confirmed, and asymptotic and approximate expressions valid within the weak and strong damping limits are developed. The problem provides an accessible account of the increasingly applicable Lambert W function and highlights much of the important mathematics associated with this simple yet rapidly emerging 'implicitly' elementary function.

Original languageEnglish
Pages (from-to)411-431
Number of pages21
JournalInternational Journal of Mathematical Education in Science and Technology
Volume37
Issue number4
DOIs
Publication statusPublished - Jun 15 2006

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Education
  • Applied Mathematics

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