Euler Rotation. Angular Momentum. The angular momentum J is defined in terms of the inertia tensor and angular velocity. All rotations included The angular momentum need not be collinear with the angular velocity. Not along principal axis Not at center of mass . p. J. r.
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Three moments of inertia
Simplified angular momentum terms
Redo the torque equations.
These are Euler’s equations of motion.Euler Equations
Select three separate rotations about body axes
Rotation of f about e3 axis.
Rotation of q about e1 axis.
Rotation of y about e3 axis.
These are the Euler angles.Euler Angles
The equivalent matrix operation is the product of three separate operations.Euler Matrices