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Home » Problems » FlatEarthDrag




Contributor:  J.R. Cash, Davy Hollevoet, F. Mazzia, A. N. Abdo
Discipline:  Aereospace
Accession:  2014




Short description:

Launch into circular orbit from a flat Earth including athmosferic drag.

Applicable solvers:



Plots of the solution <- click to generate the plots of the solution and the textual output


Mathematical description:


The problem aims to minimize the launch time of a satellite, assuming the Earth is flat and we have a uniform gravitational field g.

We need to find the control variable \alpha.

The drag is: D=fract{1}/{2}\rho C_d AV^2

where C_d is the drag coefficient (assumed constant) and A is the cross sectional area.

In order to minimize J=t_f we use these conditions:

We define the problem with:

z_1 = x  z_2 = y  z_3 = v_x  z_4 = v_y  z_1 = \lamba_2  z_6 = \lambda_3  z_7 = \lambda_4 

and we get this matrix:

With \eta=(\rho _0C_0A)/2, \beta=h/h_{scale}, t_f=z_8

The boundary conditions are obtained from:






James M LonguskiJosé J. Guzmán,  John E. Prussing Optimal Control with Aereospace Applications, Springer, Space Technology Library, v. 32, 2014 ISBN: 978-1-4614-8944-3 (Print) 978-1-4614-8945-0 (Online)