The 3 DOF of angular acceleration - RC Groups
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Feb 01, 2013, 09:49 PM
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# The 3 DOF of angular acceleration

So far out of the 6-DOF, we've discussed the 3-DOF of translational acceleration disturbances. Let's turn for a minute to the 3 -DOF of angular acceleration disturbances. Keep in mind that our gimbal so far has no closed-loop torquer motors to restore position, and let me also say that the example gimbal has frictionless pivot bearings and no cabling between aircraft frame and the outer or inner gimbal axis.

Observe the video here;

 Angular Accel Only (0 min 13 sec)

What happens? Under angular acceleration where the center of the acceleration is coincident with the axis pivot, the gimbal axis will remain stationary, fixed staring at its intended target. This is because the frictionless bearings transfer no torque from the moving frame to the camera axis.

Why?
T=Ia. Or torque equals inertia times acceleration. Where torque is in Newton meters (N-m), MOI is in Kilogram meters (Kg-m), and angular acceleration is in radians per second per second (rad/sec-sq). Simply rearranging we find that a=T/I. Thus for angular acceleration disturbances as described above, in the presence of any MOI, and the absence of torque transfer; there will be no angular acceleration imparted to the inner camera axis.
Last edited by otlski; Feb 01, 2013 at 10:08 PM.