Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1202.70122
Xu, Ming; Xu, Shijie
$J _{2}$ invariant relative orbits via differential correction algorithm. (English)
[J] Acta Mech. Sin. 23, No. 5, 585-595 (2007). ISSN 0567-7718; ISSN 1614-3116/e

Summary: This paper describes a practical method for finding the invariant orbits in $J _{2}$ relative dynamics. Working with the Hamiltonian model of the relative motion including the $J _{2}$ perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth's orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between $J _{2}$ invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte-Carlo simulation.

MSC 2000:: *70M20 Orbital mechanics

Keywords: formation flying; $J _{2}$ invariant orbit; differential correction; formation configuration

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]