An exact solvable model of rocket dynamics in atmosphere

• Autores: H. Rodrigues, M.O. Pinho, D. Portes Jr., A. Santiago
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 40, Nº. 4, 2009, págs. 523-532
• Idioma: inglés
• DOI: 10.1080/00207390802419560
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• Resumen

  • In basic physics courses at undergraduate level, the dynamics of self-propelled bodies is presented as an example of momentum conservation law applied to systems with time-varying mass. However, is often studied the simple situation of free motion or the motion under the action of a constant gravitational field. In this work, we investigate the more realistic case of time-dependent motion of an ascending rocket subjected to a quadratic drag exerted by the earth atmosphere. Interestingly, the resulting rocket equation of motion falls into a Riccati equation. Detailed solutions of the model differential equations are presented and discussed.