Moon Landing Simulation

plane

space

initial height (km)

ξ

1

200

initial speed (km/s)

ξ

2

0

initial mass (kg)

m

0

250

time (s)

t

0

time (s)	0	height (km)	200.000	τ (s)	470.079	T (s)	517.409
speed (km/s)	0.000	mass (kg)	250	α (s)	47.330

front view

expanded view (zoom)

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.

T

is the total time of descent,

τ

is the time before starting the engine, and

α=T-τ

is the time the engine is on.