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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Modeling Rocket Flight In The Low-Friction Approximation, Logan White
Modeling Rocket Flight In The Low-Friction Approximation, Logan White
Undergraduate Journal of Mathematical Modeling: One + Two
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 …
Blood Alcohol Content, Chris Ludwin
Blood Alcohol Content, Chris Ludwin
Undergraduate Journal of Mathematical Modeling: One + Two
Given a set of differential equations describing blood alcohol content as a function time, we integrated the equations to obtain a general solution. The general solution equation depends on three free parameters: the initial concentration of alcohol in the stomach after ingestion, the rate of alcohol absorption into the blood stream and the rate at which the alcohol is metabolized by the liver. We fitted our solution to experimental data to determine the unknown parameters for a particular subject.