Find Euler Angles

An interactive demo for learning and visualizing 3D coordinate transformations and Euler angles.

findEulerAngs generates Euler angle sets and animates rotations in response to user manipulation of a 3D rigid body (a box).

Use the mouse to change the orientation of the box. A wireframe of the original box position will appear. The 'Euler Axis' button animates the rotation about the Euler Axis between the original and
new box positions. The 'Rotate' button calculates a set of Euler angles for the rotation type currently selected ('Body' or 'Space') and the axis set selected in the dropdown menu to orient the axes to
the new box position. 'Derotate' reverses this process and brings the axes back to their previous position.
Once the axes have been rotated, subsequent rotations are calculated
from this new orientation. This means that Space rotations use the coordinate system associated with the previous cube orientation (i.e. the axes of the wireframe cube). 'Axes DCM' is the direction cosine matrix of the current axes orientation in the unrotated inertial frame. 'Box DCM (inertial)'
is the DCM of the box's current orientation in the unrotated inertial frame. 'Box DCM (Axes)' is the matrix product of the previous two DCMs. The Euler axis is calculated in the unrotated inertial frame.