# Convert velocity vector to yaw roll pitch Tait Bryan

I have a cartesian position and velocity vector describing the flight path of an object in the format "time posX posY posZ velX velY velZ" and want to convert it to a "time posX posY posZ ang1 ang2 ang3" (losing the absolute velocity information). I have found this answer which pretty much shows what I want - only in the opposite direction.

Is there a way to calculate the yaw, pitch and roll angles from the velocity vector? What I have is the velocity vector before rotation and the velocity vector after rotation (absolute velocity in x-direction, 0 velocity in the other directions).

\begin{align} R_z(\theta) R_x(\phi) R_y(\psi) \begin{pmatrix} u \\ v \\ w \end{pmatrix} &=\begin{pmatrix} \sqrt{u^2+v^2+w^2} \\ 0 \\ 0\end{pmatrix}\end{align}

I have found also this excellent page, I could not get to the point where I understood how I can extract the angles from the two vectors.

I have found a similar question here and will try to solve the question using the only answer which is also marked as the best answer.

• Write the velocity in spherical coordinates. – lightxbulb Jan 16 at 9:03