New definitions of 3D acceleration and inertial mass not violating F=MA in the Special Relativity

Newton’s II Law of Dynamics is a law of motion but also a useful definition of force (F=MA) or inertial mass (M=F/A), assuming a definition of acceleration and parallelism of force and acceleration. In the Special Relativity, out of these three only the description of force (F=dp/dt) does not raise doubts. The greatest problems are posed by mass, which may be invariant rest mass or relativistic mass or even directional mass, like longitudinal mass. This results from breaking the assumption of the parallelism of force and standard acceleration. It turns out that these issues disappear if the relativistic acceleration A is defined by a relativistic velocity subtraction formula. This basic fact is obscured by some subtlety related to the calculation of the relativistic differential of velocity. The reference to a non-resting system generates a little different velocity subtraction formulae. This approach confirms Oziewicz binary and ternary relative velocities as well as the results of other researchers. Thus, the relativistic three-dimensional acceleration is neither rest acceleration, nor four-acceleration, nor standard acceleration. As a consequence, inertial mass in any direction of the force has the same value as relativistic mass. In other words, the concepts of transverse mass and longitudinal mass, which depend on velocity, have been unified. In this work a full relativistic equation is derived for the motion of a body with variable mass whose form confirmed the previously introduced definitions.