A note on potential energy in non-relativistic frames

We show that, when associated with conservative forces that depend on two points in space: the center of the force and the position of the particle under its action, the value of potential energy is the same, up to an additive constant, in all frames of reference connected through an extended Galilean transformations. It is also assumed that this conservative force’s direction is parallel to the straight line connecting the particle to this force’s center. For both inertial and non-inertial frames, the result shown in this note is valid.

Keywords
Classical Mechanics; potential energy; extended Galilean transformations; conservative forces; inertial and non-inertial frames; mechanical energy