Quaternions are new to me, so I constructed a simple model to help grasp the concept. I have a very simple dynamic model that used Euler's equations for the rigid body dynamics. The model only considers attitude; translational motion is ignored. I am making use of quaternions to describe the attitude of the body, but I am having problems with the rate quaternion. Using quaternions for performing transformations is straightforward and I understand that. I've ran across a few different equations for calculating dq/dt, but the difference is mainly how you write the quaternion and whether or not you use quaternion math. Anyways, the form I've had the most luck with is dq(t)/dt = 1/2*W(t)*q(t), where W(t) is the angular velocity vector (composed as a quaternion) of the body wrt the fixed coordinates. Found here: http://www.euclideanspace.com/physics/kinematics/angularvelocity/QuaternionDifferentiation2.pdf The problem I am having is that none of my resulting quaternions are unity, which they should be. I've looked everywhere for calculating the derivative (including Kuipers), and I can't seem to find anything. The dynamics seem to behave correctly, but I know something is off. Can someone point me in the right direction?