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Fourier Series Approximations to J2-Bounded Equatorial Orbits
Joint Authors
Wang, Wei
Yuan, Jianping
Chen, Zheng
Chen, Changchun
Zhao, Yanbin
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-02-23
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Wang, Wei& Yuan, Jianping& Zhao, Yanbin& Chen, Zheng& Chen, Changchun. 2014. Fourier Series Approximations to J2-Bounded Equatorial Orbits. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-481396
Modern Language Association (MLA)
Wang, Wei…[et al.]. Fourier Series Approximations to J2-Bounded Equatorial Orbits. Mathematical Problems in Engineering No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-481396
American Medical Association (AMA)
Wang, Wei& Yuan, Jianping& Zhao, Yanbin& Chen, Zheng& Chen, Changchun. Fourier Series Approximations to J2-Bounded Equatorial Orbits. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-481396
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-481396