Initial value and two point boundary value solutions to the Clohessy-Wiltshire equations

The nonhomogeneous Clohessy-Wiltshire (C-W) equations are formulated and solved as an initial value problem in the form structure of linear systems theory. The state transition matrix (STM) and its inverse are obtained explicitly in both Newtonian and Hamiltonian form. It is shown that the STM for the C-2 equations possesses a special property making its inverse easily obtainable. Since solutions to the C-W equations are needed in two-point boundary value form to construct a good mission design tool for orbit transfer, the Lambert problem is solved in the context of the C-W equations.