โ Scribed by Hiroshi Okamura; Tadayuki Ohta; Toshiei Kimura; Kichiro Hiida
No coin nor oath required. For personal study only.
The equations of motion of a test particle moving near the center of a massive rotating ring are derived up to the post-post-Newtonian order of approximation, by using the metric tensor for many body system which is Minkowskian at spatial infinity. Logarithmic divergences due to self-interaction of the ring appear in the equations of motion. These divergences can be removed by the procedure which is similar to the renormalization method in particle physics. In the equations of motion there appears a force directing to the rotation axis and depending on the angular velocity of the ring. This force vanishes when the magnitude of the gravitational constant times the mass of the ring divided by the radius of the ring is about one tenth of the square of the velocity of light. Under this condition it is shown that the relative magnitude of the Coriohs force to the centrifugal force in the equations of motion agrees with the expected one from the equations of motion in a rotating reference frame.
๐ SIMILAR VOLUMES
It is shown that up to the second order in the gravitational constant the effect of a rotating mass shell on a particle moving near its axis is the same as that of a rotating coordinate system. Coriolis force and centrifugal force have, contrary to the case discussed by Thirring[l, 21, the value exp