Abstract
The relevance of the Central - force motion in the macroscopic and microscopic frames warrants a detailed study of the theoretical mechanics associated with it. So far, researchers have only considered central - force motion, as motion only in the translational and rotational elliptical plane with polar coordinates. However, the theoretical knowledge advanced by these researchers in line with this type of motion is scientifically restricted as several possibilities are equally applicable. In order to make the mechanics of a Central - force motion sufficiently meaningful, we have in this work extended the theory which has only been that of translational and rotational in the elliptical plane, by including fictitious radii and spin oscillations of the body about the axis of rotation. In this work, we used the methods of Newtonian mechanics to establish the new central-force field obeyed by the motion of a body, when the effect of spin oscillation is added. The new central-force field comprises of the radial accelerations, translational orbital angular velocity and the oscillating spin angular velocities. The energy conveyed in the spin oscillating phase increases as the orbital oscillating angles above or below the horizon of the elliptical plane is increased.
Highlights
The forces of nature are unbalanced and are in a state of non-equilibrium
In order to make the mechanics of a Central - force motion sufficiently meaningful, we have in this work extended the theory which has only been that of translational and rotational in the elliptical plane with polar coordinates (r, ), by including vertical spin oscillations
In order to make the theory of Central - force motion adequately meaningful, we have in this study extended the theory which has only been that of translational and rotational in the elliptical plane with coordinates (r, ), by including fictitious radii and spin oscillations (r1, r2 ;, ) about the axis of rotation
Summary
The forces of nature are unbalanced and are in a state of non-equilibrium. The difference in elliptic motion of the planets around the perihelion and aphelion is a consequence of the non-uniform and unbalanced nature of this force. A body undergoing a central force motion in an unbounded region of space induces electrostatic potential on the path of its motion. This potential creates a dipole moment which tends to oscillate the body up and down about a given equilibrium position. Consequent upon this, the body would certainly have a definite memory of the repeated path and directions of motion even in the absence of any immediate directional driving force. The up and down oscillation of a body in a central force field, with example the earth could be what is responsible for the several phenomena such as the solitary wave, tidal wave and ocean current experience in nature
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