# deuler_dt_NED¶

Warning

Based on a NED frame

Rate of change of the Euler angles in time for a given angular velocity in A frame $$\omega^A=[p, q, r]$$.

$\begin{split}\begin{bmatrix}\dot{\phi} \\ \dot{\theta} \\ \dot{\psi}\end{bmatrix} = \begin{bmatrix} 1 & \sin\phi\tan\theta & \cos\phi\tan\theta \\ 0 & \cos\phi & -\sin\phi \\ 0 & \frac{\sin\phi}{\cos\theta} & \frac{\cos\phi}{\cos\theta} \end{bmatrix} \begin{bmatrix} p \\ q \\ r \end{bmatrix}\end{split}$

Note

This function is defined in a North East Down frame which is not the typically used one in SHARPy.

param euler

Euler angles $$[\phi, \theta, \psi]$$ for roll, pitch and yaw, respectively.

type euler

np.ndarray

returns

Propagation matrix relating the rotational velocities to the euler angles.

rtype

np.ndarray