If anyone is familiar with (or has nearby) Goldstien's Mechanics text, I am having some difficulty seeing why equation 1-34 is true.
Can someone explain or perhaps hint as to why, in the given context, the gradient of a potential function of distance (in terms of a difference of position vectors) equals the difference in position vectors times an arbitrary scalar function?
Perhaps I should also lay out some other inquiries I had regarding this discussion:
Part of Goldstein's development of the internal potential energy for a system of a system of particles is motivated by "sasifying the strong law of action and reaction." Is this satisfaction a necessary feature of conservative fields, or he is simply doing this because many typical fields satisfy this criteria? (page 10 of edition 2)
The Attempt at a Solution