Euler's
Theorem on Rotations
The adjoining animation is meant to
illustrate
Euler angles and Euler's theorem on rotations. The animation shows a
frame being rotated from its initial orientation (shown in blue) to its
final orientation (shown in black) in two different ways. In the first,
the frame is rotated by a sequence of three rotations, the first about
the Z axis (dashed line), second about the Y axis (solid line), and the
third about the X axis (dotted line). The corresponding angles of
rotation are the 3-2-1 Euler angles (called yaw, pitch and roll in flight dynamics)
describing the orientation of the black frame relative to the blue
frame. Next, the animation shows that the same orientation change can
be achieved by a single rotation about a resultant axis (not shown),
thus illustrating Euler's theorem on rotations.
The animation appearing on this page was created with help from
Debashish Bagg.