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- Title
Fourier Series Approximations to J<sub>2</sub>-Bounded Equatorial Orbits.
- Authors
Wei Wang; Jianping Yuan; Yanbin Zhao; Zheng Chen; Changchun Chen
- Abstract
The current paper offers a comprehensive dynamical analysis and Fourier series approximations of J2-bounded equatorial orbits. The initial conditions of heterogeneous families of J2-perturbed equatorial orbits are determined first. Then the characteristics of two types of J2-bounded orbits, namely, pseudo-elliptic orbit and critical circular orbit, are studied. Due to the ambiguity of the closed-form solutions which comprise the elliptic integrals and Jacobian elliptic functions, showing little physical insight into the problem, a new scheme, termed Fourier series expansion, is adopted for approximation herein. Based on least-squares fitting to the coefficients, the solutions are expressed with arbitrary high-order Fourier series, since the radius and the flight time vary periodically as a function of the polar angle. As a consequence, the solutions can be written in terms of elementary functions such as cosines, rather than complex mathematical functions. Simulations enhance the proposed approximation method, showing bounded and negligible deviations. The approximation results show a promising prospect in preliminary orbits design, determination, and transfers for low-altitude spacecrafts.
- Subjects
EQUATORIAL satellites; FOURIER series; APPROXIMATION theory; ELLIPTIC integrals; ELLIPTIC functions
- Publication
Mathematical Problems in Engineering, 2014, p1
- ISSN
1024-123X
- Publication type
Article
- DOI
10.1155/2014/568318