Research Paper: Analytical Solution of the Equation Related to the Oscillations of Ap Pulsating Stars Under the Effect of Rotation

Rapidly oscillating Ap stars are a special type of variable stars that are not in hydrostatic equilibrium. Their pulsation period is very short compared to other stars of this group and is less than one hour. These stars have spectral type A and lines related to rare-earth elements are increasingly observed in their spectrum, so they are known as Ap stars. In this research, the equation of motion of the rapidly oscillating Ap star was solved using the perturbation method in the presence of a smooth and uniform rotation and it was determined that under the effect of rotation in the stellar system, the modes are coupled among themselves. Each mode with a specific l is separated into 2l+1 modes due to rotation, and each of these modes under disturbance does not correspond to a specific value of m, but each mode under perturbation consists of a linear combination of m=2l+1modes.