Please help me solve a problem that has puzzled me for years. I am not a mathematician or a physicist, so please bear with me. Imagine the apparatus pictured to be a depiction of the x, y and z axes. The x is represented by the green stick. The y is represented by the yellow stick, and the z by the blue stick. Let’s place an arbitrary range of each axis as -10 to +10. At -10 and +10 of each axis is a potential force represented by the arrows. When applied, it will be a constant force, such that when initiated in one axis only to the points at -10 and +10 that axis would scribe a circle. Now imagine a hypothetical sphere “enclosing” the apparatus whose x, y and z axes would correspond exactly to the x, y and z axes of the stationary apparatus. The imaginary sphere will never move, and will serve as a reference or standard. So the center of the imaginary sphere is x=0, y=0 and z=0…the same co-ordinates of the center point of the stationary apparatus. Now, apply an equal and constant force to each axis in the direction of their arrows at exactly the same moment. With no “knowledge” of the other axes, any one axis will always “think” that it is fulfilling its mission of scribing a circle. Please forgive the anthropomorphism. Questions: Will the center point of the apparatus remain at the center point of the imaginary sphere or be displaced in a particular direction? Since the end points of each axis will no longer scribe a circle, what will be the trajectory of each end point? Will the end points of each axis scribe identical paths? If this force could be applied indefinitely, would the end points eventually scribe a sphere? If you reverse the direction of the forces on just one axis, how will it affect the behavior of the apparatus? Thank you!