FlatEarthDrag

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

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

twpbvpc,twpbvplc,colsys,colnew,bvp_m2

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:

with

References

James M Longuski, José 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)

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