Analytical velocity hodograph of projectile motion under polynomial drag

نویسندگان

چکیده

Abstract Velocity hodographs are of importance in weather analysis. A historically important case is the hodograph Kepler problem. Here, we explore analytical solutions for velocity projectile trajectories under a polynomial, velocity, hydrodynamic dissipation. General terms hypergeometric functions found odd powers monomial terms. The even have but do not find general expression them. For completeness include constant or Coulomb case, as well its sum with linear and quadratic cases. Both shown explicit angle. Usually discussed textbooks articles, here that more cases admit solutions, when position time cannot be obtained explicitly they need numerical integration. Furthermore, motion and, additional drag could used to design new university lab experiments.

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ژورنال

عنوان ژورنال: Journal of physics

سال: 2022

ISSN: ['0022-3700', '1747-3721', '0368-3508', '1747-3713']

DOI: https://doi.org/10.1088/1742-6596/2307/1/012019