  Maneuvering a spacecraft in the cislunar space is a complex problem, since it
is highly perturbed by the gravitational influence of both the Earth and the
Moon, and possibly also the Sun. Trajectories minimizing the needed fuel are
generally preferred in order to decrease the mass of the payload. A classical
method to constrain maneuvers is mathematically modelling them using the Two
Point Boundary Value Problem (TPBVP), defining spacecraft positions at the
start and end of the trajectory. Solutions to this problem can then be obtained
with optimization techniques like the nonlinear least squares conjugated with
the Theory of Functional Connections (TFC) to embed the constraints, which
recently became an effective method for deducing orbit transfers. In this
paper, we propose a tangential velocity (TV) type of constraints to design
orbital maneuvers. We show that the technique presented in this paper can be
used to transfer a spacecraft (e.g. from the Earth to the Moon) and perform
rendezvous maneuvers (e.g. a swing-by with the Moon). In comparison with the
TPBVP, solving the TV constraints via TFC offers several advantages, leading to
a significant reduction in computational time. Hence, it proves to be an
efficient technique to design these maneuvers.
