# Reverse Quaternion Kienmatics equations

by zuba
Tags: equations, kienmatics, quaternion, reverse
 P: 1 Hi all!, first post! I'm programming an attitude estimation and control algorithm for a satellite. So I need a reference "trayectory" for my control system to try to follow. The generation of that attitude profile is tricky: point to the sun, if sat has access to a certain city, point to it, the point again to the sun... and so on. So I've managed to make a q(t) to make all that possible, but I need the angular velocities that yield that reference attitude quaternion as a function of time. While I have already figured out a way to get them, they are not perfectly mathematically calculated, showing some nasty discontinuities at certain times. So, the problem is, given the quaternion kinematic equations: \dot q =\frac{1}{2} \left[ \begin{array}{cccc} q_4 & -q_3 & q_2 & q_1 \\ q_3 & q_4 & -q_1 & q_2 \\ -q_2 & q_1 & q_4 & q_3 \\ -q_1 & -q_2 & -q_3 & q_4 \end{array}\right] \left[ \begin{array}{c} \omega_1 \\ \omega_2 \\ \omega_3 \\ 0 \end{array}\right], and the quaternion $$q(t),$$ what is $$\vec \omega(t)?.$$ I think the problem would be a boundary value problem, but I don't really know. Does anyone can point me in the right direction?? maybe a matlab supereasy command ? Thanks in advance!!

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