In a realistic model for rocket dynamics, in the presence of atmospheric drag and altitude-dependent gravity, the exact kinematic equation cannot be integrated in closed form; even when neglecting friction, the exact solution is a combination of elliptic functions of Jacobi type, which are not easy to use in a computational sense. This project provides a precise analysis of the various terms in the full equation (such as gravity, drag, and exhaust momentum), and the numerical ranges for which various approximations are accurate to within 1%. The analysis leads to optimal approximations expressed through elementary functions, which can be implemented for efficient flight prediction on simple computational devices, such as smartphone applications.
"Modeling Rocket Flight in the Low-Friction Approximation,"
Undergraduate Journal of Mathematical Modeling: One + Two:
1, Article 5.
DOI: http://dx.doi.org/10.5038/2326-36126.96.36.19961 Available at: http://scholarcommons.usf.edu/ujmm/vol6/iss1/5
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Manoug Manougian, Mathematics and Statistics
Razvan Teodorescu, Physics