Well no.No it doesn't & saying yes it does is nothing but shit talk by shit talkers.
Charles, what you are doing here is being incredibly stubborn and aggressive. We have provided a lengthy list of pendulums that behave exactly as expected, with the plane of oscillation rotating according to the latitude. If you could point us to any which does NOT follow this rule, without strong interference from things like air movement, that would be something important and, to be honest, very surprising.
By the way, what do you mean by
Momentum & torque developed which is instigated by the first swing of the pendulum. ? You surely do realize that there are only three general ways of starting the pendulum after pulling it to the side:
1. letting it go, without applying any additional force to it
2. giving it a slight push in the exact direction towards the point below the pivot/anchor/whatever it should be called point - meaning no initial velocity in any plane other than the one described by the starting point, the pivot point and the directly-below-pivot point
3. pushing it in any other direction, giving it an initial velocity component not in the previously mentioned plane
The first two will give a similar-looking arc trajectory in the starting plane. The only difference would be that the second one would swing in a wider arc. When viewed from top, it would be a straight line. It would be very slightly curved on each cycle if the Earth rotated, it would remain straight if the Earth was stationary, regardless whether it was flat or round.
The last one would immediately give you an elliptic trajectory when seen from the top.
There is
no way of launching the pendulum so that it would follow an asteroid-like curve(viewed from top) without rotating the observer's position relative to the starting plane(which would happen with rotating Earth - again, regardless of its shape). It will either follow a straight line, or an ellipse. And as you can surely understand, an ellipse is almost the opposite of an asteroid. While moving along an ellipse, you are constantly curving "towards" the center point. While moving along an asteroid, each single curve is bending "away" from the middle.