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An exact solvable model of rocket dynamics in atmosphere

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Abstract:

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.

Keywords: differential equation; rocket dynamics; time-varying systems

Document Type: Research Article

DOI: http://dx.doi.org/10.1080/00207390802419560

Affiliations: Centro Federal de Educacao Tecnologica do Rio de Janeiro, Rio de Janeiro, RJ, Brazil

Publication date: January 1, 2009

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