A particle P of mass m moves under the simple harmonic field F=−(mΩ2r)r^, where Ω is a positive constant. Obtain the radial motion equation and show that all orbits of P are bounded.
Initially P is at a point C, a distance c from O, when it is projected with speed Ωc in a direction making an acute angle α with OC. Find the equation satisfied by the apsidal distances. Given that the orbit of P is an ellipse with centre O, find the semi-major and semi-minor axes of this ellipse.