On one resolvent method for integrating the low angle trajectories of a heavy point projectile motion under quadratic air resistance

Chistyakov V.V.
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New key parameters, namely b0 = tgθ0, θ0 — angle of throwing, Ra — top curvature radius and β0 — dimensionless speed square on the top of low angular trajectory were suggested in classic problem of integrating nonlinear equations of point mass projectile motion with quadratic air drag. Very precise formulae were obtained in a new way for coordinates x(b), y(b) and fly time t(b), b = tgθ where θ is inclination angle. This method is based on Legendre transformation and its precision is automatically improved in wide range of the θ0 values and drag force parameters α. The precision was monitored by Maple computing product.

Keywords: quadratic air drag, projectile, Legendre transformation, law angular trajectory, automatically adjusted formula precision, Maple
Citation in English: Chistyakov V.V. On one resolvent method for integrating the low angle trajectories of a heavy point projectile motion under quadratic air resistance // Computer Research and Modeling, 2011, vol. 3, no. 3, pp. 265-277
Citation in English: Chistyakov V.V. On one resolvent method for integrating the low angle trajectories of a heavy point projectile motion under quadratic air resistance // Computer Research and Modeling, 2011, vol. 3, no. 3, pp. 265-277
DOI: 10.20537/2076-7633-2011-3-3-265-277
URL: http://crm-en.ics.org.ru/journal/article/1807/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
According to Crossref, this article is cited by:
  • Viktor Vladimirovich Chistyakov. Numerical-analytical integrating the equations of a point mass projectile motion at the velocities close to sonic peak of air drag exponent. // Computer Research and Modeling. — 2013. — V. 5, no. 5. — P. 785. DOI: 10.20537/2076-7633-2013-5-5-785-798
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