Modeling the flight of a glider with Mathematica and KSP
We derive a set of differential equations to model the flight of a glider, find solutions to these equations with Mathematica, and then compare the solutions with flights in the computer game Kerbal Space Program. We also find expressions for both terminal and trim velocity by considering particular solutions to the equations. The equations derived here are sometimes referred to as Lanchester's phugoid model or Zhukovsky's (or Zhukovskii's) equations and the solutions to these equations illustrate what is referred to as longitudinal oscillation.
Special thanks to Hector Mera Couto, and his students in differential equations, for the idea to study this topic, help in developing the mathematical model, interpreting the solutions, and especially to Professor Mera Couto for developing the Mathematica code used in this video. See Professor Mera Couto's presentation at SIMIODE.org ( • Illustrating the Dynamics of Gliders ... ) on the glider model and how he has used this topic as a class project in the Differential Equations class with the free online flight simulator GeoFS.
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