Cylindrically and spherically constrained families of non-Keplerian orbits

This paper introduces new families of Sun-centered non-Keplerian orbits
(NKOs) that are constrained to a three-dimensional surface such as a cylinder or
sphere. As such, they are an extension to the well-known families of two dimensional NKOs. For both the cylindrical and spherical types of orbits, the
equations of motion are derived in an appropriate reference frame, constraints
are introduced to confine the orbit to a cylindrical or spherical surface and further constraints allow the definition of the set of feasible orbits. Additionally, the phase spaces of the orbits are explored and a numerical analysis is developed to find periodic orbits within the set of feasible orbits. The richness of the problem is further enhanced by considering both an inverse square acceleration law (mimicking solar electric propulsion) and a solar sail acceleration law to keep the spacecraft on the cylindrical or spherical surface. These new families of NKOs generate a wealth of new orbits with a range of interesting applications ranging from solar physics to astronomy and planetary observation.