# FlatEarthDrag

FlatEarthDrag | |
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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:**

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 .

We need to find the control variable .

The drag is:

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

In order to minimize we use these conditions:

We define the problem with:

and we get this matrix:

With , ,

The boundary conditions are obtained from:

with

**Download:**

- Fortran code: FlatEarthDrag.f
- matlab code:
- R code: FlatEarthDrag.R

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)