# Méthodes géometriques en mécanique spatiale et aspects numériques

Abstract : We present in this thesis two research projects
on the optimal control of the space vehicles.

In the first, we have dealt with the orbit transfer
problem. We study the minimum time control of a satellite that we want to reach a geostationary orbit. Our contribution is of two kinds. Geometric, first, since we study the controllability of the system together with the geometry of the transfer (structure of the command) by means of geometric control without state constraint tools (minimum principle). Then we present shooting
algorithm and homotopy method. These approaches allow the numerical resolution of problems with strong or low thrust satellites.

The second project concerns to the calculation of the
trajectories of atmospheric re-entry for the space shuttle. The system describing the trajectories is in dimension $6,$ the control is the bank angle or its derivative and the cost is the total thermal flux. Moreover there are state constraints (thermal flux, normal acceleration and dynamic pressure). Our study is
founded on obtaining the necessary optimality conditions (minimum principle with state constraints) applicable to our case, on the state constraint associated parameters $(\eta, \nu, u_b)$ calculation and on the analysis of the small time optimal synthesis for single input systems with state constraints. The optimal solution is numerically computed with a multiple shooting algorithm and homotopy method.
Keywords :
Document type :
Theses
Domain :

https://tel.archives-ouvertes.fr/tel-00012145
Contributor : Mohamed Jabeur <>
Submitted on : Thursday, April 13, 2006 - 10:42:06 PM
Last modification on : Saturday, December 19, 2020 - 3:03:38 AM
Long-term archiving on: : Monday, September 17, 2012 - 1:35:10 PM

### Identifiers

• HAL Id : tel-00012145, version 1

### Citation

Mohamed Jabeur. Méthodes géometriques en mécanique spatiale et aspects numériques. Mathématiques [math]. Université de Bourgogne, 2005. Français. ⟨tel-00012145⟩

Record views