A PERTURBATION THEORY USING HAMILTON'S PRINCIPAL FUNCTION: APPLICATIONS TO THE PERTURBED TWO-BODY PROBLEM
- Paper number
IAC-08.C1.3.9
- Author
Mr. Oier Penagaricano, Univesity of Michigan, Spain
- Year
2008
- Abstract
Solutions to two-point boundary value problems are of significant importance in the field of astrodynamics and have been subject to extensive research over the years. However, the lack of procedures that automatically converge to the desired solution remains as a fundamental difficulty in solving these problems. Usually, solutions involve open ended iterative methods that often have no guaranteed convergence and require a good initial guess. Examples of these methods include the method of homotopy, multiple shooting combined with Newton's iteration, and a variety of other techniques. In this work we develop an analytical perturbation technique that solves the two-point boundary value problem of a perturbed system using Hamilton's principle and Hamilton's principal function. This technique finds its applications in the two-body problem, configuration of spacecraft formations, optimal control problems, and a variety of problems in astrodynamics and other areas as well. We additionally develop a perturbation technique to analytically solve the initial value problem with s symplectic discrete Keplerian map. This technique allows for low-energy space mission design, drastically reducing the amount of fuel used, hence lowering the total cost of certain missions. Results show that this theory can be used to accurately solve the two-point boundary value problem for a spacecraft in a Keplerian orbit perturbed by oblteness of the central body, solar radiation pressure or third body effects. Results in the restricted three body problem show that our analytical technique to solve the initial value problem allows to accurately predict the change in Keplerian orbit elements over several orbits. Ross and Scheeres (2007) exposed that such analytical solutions can be used to design low energy trajectories, such as orbit transfers between bodies in close proximity. However, their approach is suited best for qualitative analysis rather than quantitative.
- Abstract document
- Manuscript document
IAC-08.C1.3.9.pdf (🔒 authorized access only).
To get the manuscript, please contact IAF Secretariat.