Moon Landing Simulation

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This Demonstration simulates the descent of a spaceship on the Moon for different values of the initial parameters. Minimizing the fuel consumed leads to an optimal control problem solved by applying Lagrange's principle and Pontryagin's maximum principle. is the total time of descent, is the time before starting the engine, and is the time the engine is on.

Contributed by: Valeriu Ungureanu and Alexandru Brega (March 2011)
Open content licensed under CC BY-NC-SA




V. A. Ungureanu, Mathematical Programming, ChiÅŸinău: CEP USM, 2001 (in Romanian).

V. M. Alexeev, Optimization Problems, Moscow: Nauka, 1984 (in Russian).

A. M. Letov, The Mathematical Theory of Optimal Processes, Moscow: Nauka, 1981 (in Russian).

E. B. Li, Fundamentals of the Theory of Optimal Control, Moscow: Nauka, 1972 (in Russian).

L. S. Pontryagin, Maximum Principle for Optimal Control, Moscow: Nauka, 1989 (in Russian).

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