Analytic Approximations of Projectile Motion with Quadratic Air Resistance

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References

[1] R. D. H. Warburton and J. Wang, “Analysis of asymptotic projectile motion with air resistance using the Lambert W function,” American Journal of Physics, Vol. 72, pp. 1404–1407, 2004.

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[6] E. Lutz, “Analytical results for a Fokker-Planck equation in the small noise limit,” American Journal of Physics, Vol. 73, pp. 968–972, 2005.

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[8] There is a solution presented in terms of the slope angle by A. Tan, C. H. Frick, and O. Castillo, “The fly ball trajectory: An older approach revisited,” American Journal of Physics, Vol. 55, pp. 37–40, 1987. But the slope angle is unknown except at the top (zero) of the trajectory, and can be found only numerically or graphically. Therefore, the solution is not in closed form.

[9] G. W. Parker, “Projectile motion with air resistance quadratic in the speed,” American Journal of Physics, Vol. 45, pp. 606–610, 1977.

[10] R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W function,” Advances in Computational Mathematics, Vol. 5, pp. 329–359, 1996.

[11] H. R. Kemp, “Trajectories of projectile motion in air for small times of flight,” American Journal of Physics, Vol. 55, pp. 1099–1102, 1987.

[12] B. Hayes, “Why W?” American Science, Vol. 93, pp. 104–108, 2005.

[13] J. Wang, To be published.

[14] M. Abramowitz and I. A. Stegun, “Handbook of mathematical functions,” Dover, New York, pp. 18, 1970.