# A rocket is started from the surface of the earth. Calculating the height as function of its mass and fuel consumption. 
# Approximation of gravity of earth by g
# Equation of motion
# r'' = alpha / (m0 - alpha*t) * v0 - g
#   alpha: fuel consumption, e.g. 2000t in 2,5 min = 13,333*10^3 kg/s
#   m0: initial mass of rocket, e.g. Saturn V: 2900 t = 2,9*10^6 kg
#   v0: the velocity of the exhaust of the rocket: 3,180*10^3 m/s
#   g: acceleration of earth = 9,81 m/s^2

include CompoundFunctions.LACE # include idivide

coefficient.1     -> alpha1
coefficient.2(+1) -> alpha2 # == alpha1
coefficient.3(-1) -> -m0
coefficient.4     -> v0
coefficient.5(+1) -> g

# generate t-ramp
iintegrate (-1) -> t

cmultiply (alpha1, t) -> alpha*t
isum (-m0, alpha*t) -> m0-alpha*t
idivide (alpha2, m0-alpha*t) -> -alpha/(m0-alpha*t)
cmultiply (-alpha/(m0-alpha*t), v0) -> -alpha/(m0-alpha*t)*v0
isum(-alpha/(m0-alpha*t)*v0, g) -> alpha/(m0-alpha*t)*v0-g

iintegrate (alpha/(m0-alpha*t)*v0-g) -> -v
invert (-v) -> v
iintegrate (-v) -> z

output (t) -> out.x
output (v) -> out.y
output (z) -> out.z