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Y
X
yaw = 90
Y
Z
X
Z
Fig. 7.11. The X Y Z axial system after a yaw of 90 .
Y
Y
X
roll =45
Z
Z
X
Fig. 7.12. The X Y Z axial system after a roll of 45 .
Y
pitch = 90
Y
X
Z
X
Z
Fig. 7.13. The X Y Z axial system after a pitch of 90 .
a yaw of 45 about the z -axis, it would rotate the x -axis towards the x -axis,
counteracting the effect of the original roll. yaw has become a negative roll
rotation, caused by the 90 pitch. This situation is known as gimbal lock ,be-
cause one degree of rotational freedom has been lost. Quite innocently, we
have stumbled across one of the major weaknesses of Euler angles: under cer-
tain conditions it is only possible to rotate an object about two axes. One
way of preventing this is to create a secondary set of axes constructed from
three orthogonal vectors that are also rotated alongside an object or virtual
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