How have you applied the force in your simulation? The 2 images that you provided look to be different in terms of application of the force. In the left one the force is along the central axis, while in the second one it is on a offset distance. Both these cases are different. "... namely, the horizontal component cancels when I integrate over 360 degrees. Do you agree? Is this what were you saying?" - yes this is what I meant.
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