Motion in rotating Earth: exact solutions and second-order effects of noninertial forces

The motion of a particle evaluated from the noninertial frame rotating Earth with constant angular velocity ω is solved analytically without carrying out priori approximations, that is, considering both Coriolis and centrifugal terms. Position vector solutions written in terms generic initial conditions were obtained decoupled sixth-order equation motion, using fully vectorial approach, specifically resorting to coordinates. By comparing exact for complete approximate (ignoring term beginning) problems, great differences can be seen order differential as well temporal dependencies solutions. Noninertial effects solution classified according magnitude ω, where first-order are oriented east-west second-order ones north-south.