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1. The problem statement, all variables and given/known data

Question 1: given a rigid tetrahedron, with vertices A, B, C and D anchored to their initial locations with an arbitrary but uniform spring constant, will Cases 1, 2, and 3 below result in the same behavior of the system?

- Case 1: a force of constant magnitude (red vector) applied to point A, and whose orientation relative to the tetrahedron is constant (if the tetrahedron moves, the force vector moves with it, as if there is a theoretical rocket engine fixed to the tetrahedron at point A).

- Case 2: the individual components of the force vector from Case 1, in the direction of points B, C, and D respectively (brown vectors), applied to point A in the same manner as before.

- Case 3: the same components from Case 2, but now applied respectively to points B, C, and D (green vectors) in the same manner as before.

If "yes" to question 1:

Question 2: if the rigid object is also anchored with same spring constant at additional points (the object is no longer necessarily a tetrahedron), will all cases still result in the same behavior? The additional points have no rocket-like forces applied to them.

Question 3: if the object is not perfectly rigid, will all cases still result in a similar behavior?

2. Relevant equations

A set of force vectors applied to a given point will have the same effect as a single force vector which is the sum of the vectors in the set applied to the same point.

A force has the same effect on a system regardless of of where it is positioned along its line of action.

These are principles that apply to static systems, however my assumption is that since the forces always preserve their orientation relative to the tetrahedron, they will be equivalent at any given instant in time and therefore the static principles will apply.

3. The attempt at a solution

I'm attempting to use this scenario to verify the accuracy of a physical simulation. My assumption is that they should all result in the same behavior, and (since the simulation has a small damping factor) the tetrahedron should stabilize to the same location in all cases. However when I run Case 3, the tetrahedron ends up in a very different location, so I'm posting this question here to check my assumptions.

Please let me know if you believe this post is more appropriate on a different forum. It is not homework, but I believe it may fall under the category of "homework-like."

Thanks in advance!

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# Homework Help: Force equivalency in a physical simulation

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