Spacecraft Mission Design
Mission design combines dynamics, control theory, and computation.
Newton’s laws and computational tools are used to design spacecraft orbits to explore our solar system. Onboard controls are used to change the velocity and orientation of a spacecraft.
When Newton’s equations of motion are formulated as a Hamiltonian system, the constant energy levels of the Hamiltonian are invariant with respect to the dynamics. Velocity changes can be used to change energy levels. For example one may want to travel from a circular low earth orbit to another circular orbit of larger radius. The Hohmann transfer does this using an elliptic orbit tangent to both circular orbits. The velocity changes are made at the tangency points. In general going from an initial condition or invariant set on one energy level of a Hamiltonian system to a final condition or invariant set on another level of the system with constraints on changes in velocity and transfer time is the problem that will be discussed in the context of the circular restricted three-body problem.