**Description**

The Shoot package is a fortran package for solving Two Points Boundary
Value Problems by the shooting method. The second member of the TPBVP can be discontinuous. In
this case we use dense output of the numerical integration of Initial
Value Problem to detect the schwitching times and the derivatives are
calculated rigorously using variational equations [1].
An application to the numerical solution
of continuous 3D maximum mass orbit transfer around the Earth , especially for low thrust engines (e.g., thrust of
Newton for a 1500 Kilogramme satellite) is given. The optimal control model given
by the French Space Agency is the following
(we refer to [2] for details):

m_{f}
-> max

dx/dt = f_{0}(x)+1/m
(u_{1}f_{1}(x)+u_{2}f_{2}(x)+u_{3}f_{3}(x)),
t in [0,t_{f}]

dm/dt = -ß|u|

x(0) = x^{0},
m(0) = m^{0}, h(x(t_{f})) = 0

|u| <= T_{max}

where T_{max} is the maximum modulus of the thrust. The state
of the satellite is described by the geometry of the ellipse osculating
to the trajectory and its position on it, x = (P,e_{x},e_{y},h_{x},h_{y},L),
and by its mass m.

**References**

[1] P. Martinon and J. Gergaud, *Using switching detection and variational equations for the
shooting method*,
Optimal Control, Applications and Methods, 28(2) (2007), pp. 95-116.

**Download**

Shoot-1.1.tar

Shoot package v1.1 - User Guide

P. Martinon and J. Gergaud

Technical Report RT/APO/08/03, INP-ENSEEIHT-IRIT, July 2008

gergaud@enseeiht.fr, martinon@cmapx.polytechnique.fr