Tangent orbit technique in three dimensions

The tangent orbit technique in three dimensions (3D) is studied. Based on a new definition of tangent orbits in 3D, three orbit transfer problems are solved, including tangent to initial orbit, tangent to final orbit, and cotangent transfer. By solving the flight-direction angle, the tangent to initial/final orbit problem is analytically solved. However, the cotangent transfer problem in 3D is solved by a numerical iterative algorithm. Unlike the tangent orbit technique in two dimensions (2D), the flight-direction angles of two tangent orbits in 3D are not equal. The single solution of the cotangent transfer in 2D can be solved in closed form, whereas in 3D there may exist several solutions which can only be solved by a numerical iterative algorithm. For the tangent to initial/final orbit problem the conditions are solved only by a numerical iterative algorithm, whereas for the cotangent transfer problem the conditions cannot even be directly obtained.