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Angular acceleration to "orient"

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I have a set of points that contain "linear" and "angular" acceleration data of a moving object.
Point 0 - 1 frame
Point 1 - 2 frame
Point 240 - 240 frame
It is easy to restore the motion path using linear acceleration. (Area CHOP)
Please help me figure out how to calculate object rotation angles or orientation
using "angular acceleration" or "angular velocity".
I'm totally stuck with matrices and quaternions :( so a math explanation of this process would be great!
Here the test hip to play with.


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