Abstract
In the present paper we announce a completely analytic closed-form third-order solution to the main problem in the theory of an artificial satellite. This is the first time an analytic solution of the main problem has been produced to order 3 which is valid for satellites with any eccentricity 0<Kl. The solution is accomplished by constructing a progression of three canonical transformations from the state variables to a set of action-angle variables in which the Hamiltonian for the problem is a function of the action variables only. The transformed Hamiltonian is developed, without omitting terms, to order 4 in the small parameter €= -J2; by way of verification it was found to agree through order 3 with the theory of Brouwer as extended by Kozai. The algebraic expressions for these transformations were produced by computer in a very compact form; conciseness is achieved in two ways, by eliminating the parallax and by controlling the computer automated calculations so as to avoid infinite series expansions in the eccentricity. Our programs prove that the main problem in satellite theory can be solved in closed form to order 3.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
