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## Main Question or Discussion Point

I have found that even though knowing the potential energy is vital for classical mechanics, most of the times what you know is actually the force, so you have to determine the potential energy based on that. So, here's the issue:

The relationship between the force and the potential energy is this:

##F=-\nabla V(q_{1},q_{2},...,q_{i})##

If I want to know the potential energy, what do I do? I had an idea, but I don't know if it is correct:

If ##F=-\nabla V(x,y,z)##, then V(x) is just minus the integral of F over x by treating y and z as a constant, and so on and so forth, and then if you want to know what V(x,y,z) is, you just add everything together. But then you'd get 3 different constants of integration that I don't know what they are.

Any help would be appreciated.

The relationship between the force and the potential energy is this:

##F=-\nabla V(q_{1},q_{2},...,q_{i})##

If I want to know the potential energy, what do I do? I had an idea, but I don't know if it is correct:

If ##F=-\nabla V(x,y,z)##, then V(x) is just minus the integral of F over x by treating y and z as a constant, and so on and so forth, and then if you want to know what V(x,y,z) is, you just add everything together. But then you'd get 3 different constants of integration that I don't know what they are.

Any help would be appreciated.