# Showing rotational trajectory with Python

#### Avatrin

Hi

I have a list of 3D angular velocities (a numerical solution to an ODE). I want to show the trajectory this rotation would cause by mapping it out on the unit sphere. How can I go about doing that? What is the best way to approach this?

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#### Avatrin

Okay, it looks like this may not be easy. Does anybody here have any suggestion regarding how I can show the trajectory of a rotation given the list of 3D angular velocities?

#### jartsa

Isn't it simple like this:

If a body turns 1 degree in one second around x-axis, and during that same second it also turns 2 degrees around y-axis, then the new angles are: old x-angle + 1 , old y-angle + 2

If the turning around the x-axis occurred mostly during the first half of the second and the turning around the y-axis occurred mostly during the last half of the second, that would be problematic.

Oh yes, it was simple because I considered just one sample of the many different angular velocities.

Last edited:

#### Avatrin

I should've been clearer. I don't think your issue applies in this case... I have this:

$\omega(t_n) = [\omega_x(t_n),\omega_y(t_n),\omega_z(t_n)]_{t_n \in I}$

Here $I = [0,a]$ for some real, positive number a is a closed interval. So, if, for some closed subinterval, the turning occured along the x-axis before the y-axis, that information already is contained in my list.

Also, my initial condition for position is any point on the unit sphere. So, lets say the north pole. I want to see how the north pole moves around given the angular velocities I have available.

"Showing rotational trajectory with Python"

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