[ODE] Balance of torque

[Gib Bogle]

I'm simulating the motion of a heavy rope spinning about a vertical 
axis.  The rope is represented as a number of rods connected by 
ball-and-socket joints, and the two ends are connected to the vertical 
axis by hinge joints.  The motion is driven by external applied forces 
on the rods.  A constant rotational speed is maintained by suitable 
application of a resisting torque (applied as a force in each timestep) 
on one of the rods that is hinged to the axis (the other is free).

The behaviour looks fine, but there is a discrepancy in the torque 
balance.  Since the rotational speed is held almost constant, the net 
torque of the applied forces, averaged over one rotation, should match 
the resisting torque, averaged in the same way.  (There is no air 
drag.)  In fact these two average torques are roughly in the ratio 43:38.

I'd like to know the explanation for this discrepancy, and also if there 
is a way to reduce it. 

Thanks
Gib