Forced precession orbit departing from Keplerian orbit under continuous normal thrust

A novel non-Keplerian orbit, known as forced precession orbit, resulting from continuous normal thrust is proposed motivated by the precession of gyroscope. We study the orbits departing from both Keplerian circular orbit and elliptical orbit. For the circular case, the forced precession rule we defined indicates that constant normal thrust is required, while for the elliptical case, periodic normal thrust is required. Using a quaternion-based formulation, the orbital motion in the circular case can be solved analytically, which is not true of the elliptical case. Therefore, numerical analysis and Floquet theory are employed to determine the orbital characteristics in the elliptical case. The results indicate that the forced precession orbit in the circular case is a displaced orbit. The long-term evolution of the forced precession orbit in the elliptical case exhibits a quasi-bird's nest geometry with upper and lower circular boundaries, the radii of which can be determined using the integral constants. Using appropriate initial orbital parameters, a quasi-periodic, displaced orbit parallel to the equatorial plane with zonal coverage can be obtained in the elliptical case.