A Scalar Equation of Motion

In classical mechanics, this thread presents a scalar equation of motion, which can be applied in any reference frame (rotating or non-rotating) (inertial or non-inertial) without the necessity of introducing fictitious forces.

If we consider two particles A and B of mass and respectively, then the scalar equation of motion, is given by:





where and are the velocities of particles A and B, and are the accelerations of particles A and B, and are the positions of particles A and B, and and are the net forces acting on particles A and B.

This scalar equation of motion is invariant under transformations between reference frames.

In addition, this scalar equation of motion would be valid even if Newton's three laws of motion were false.