Spacecraft Formation Dynamics and Design

Previous research on the solutions of two-point boundary value problems is applied to spacecraft formation dynamics and design. The underlying idea is to model the motion of a spacecraft formation as a Hamiltonian dynamic system in the vicinity of a reference solution. Then the nonlinear phase flow can be analytically described using generating functions found by solving the Hamilton‐Jacobi equation. Such an approach is very powerful and allows the study of any Hamiltonian dynamical systems independent of the complexity of its vector field and the solution of any two-point boundary value problem to be solved using only simple function evaluations. The details of the approach are presented through the study of a nontrivial example, the design of a formation in Earth orbit. For the analysis, the effect of the J2 and J3 gravity coefficients are taken into account. The reference trajectory is chosen to be an orbit with high inclination, i = π/3, and eccentricity, e = 0.3. Two missions are considered. First, given several tasks over a one-month period modeled as configurations at given times, the optimal sequence of reconfigurations to achieve these tasks with minimum fuel expenditure is found. Next, the theory is used to find stable configurations such that the spacecraft stay close to each other for an arbitrary but finite period of time. Both of these tasks are extremely difficult using conventional approaches, yet are simple to solve with the presented approach.

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