This paper is the author’s attempt to generalize classical (Newtonian) mechanics to take into account relatively recent gyroscopic work due to first Eric Laithwaite and later Harvey Fiala and others. Of course, Newton himself did not have any gyroscopic motion as data except the rotation of moons and planets, the orbits of comets, and the like, and -- needless to say -- such involved extremely small rpm's. Thus, he could not have discovered the gyroscopic effects that Laithwaite and the others stumbled upon even with all his brilliance. But it seems clear that his mechanics must be almost correct except in the case of very rotational motion, and so the approach of this paper will be to apply as small a "band aid" to Newtonian theory as possible and still explain the new gyro data that does not quite fit. Thus we retain his three laws, but in their original form where the force is not the mass times the acceleration but rather the time derivative of the momentum. We also retain his (implicit) vector addition of forces but not the equivalence of gravitational and inertial mass {11} … as we assume variable inertial mass. In fact, that is the only one of his basic assumptions that we do alter in that we do not assume the inertial mass of an (electrically neutral) particle is constant for non-relativistic velocities and so inertial mass may vary with motion. The paper first develops a generalized neo-Newtonian theory and then applies the theory to the general case of a gyroscope (having a thin and hollow disc rotor) with a fixed pivot, which steadily precesses (not necessarily slowly), but does not nutate, and then moves on to investigate the case of the precession angular velocity suddenly experiencing constant deceleration until the precession halts. These gyroscopic examples involve anomalous behavior and so are elementary examples of the gyroscopic results mentioned above, and their analysis will hopefully point the way to successful prediction of anomalous gyroscopic phenomena. The author hopes that his results will "get the researchers thinking in the right direction" as far as obtaining a rigorous generalization of Newton's theory capable of handling all gyroscopic data as well as that known to him from astronomy. (We, of course, restrict ourselves to considering only non-relativistic velocities here.)
