Second-Order Integral-Form Gauss's Variational Equations Under Impulsive Control Academic Article

abstract

• Copyright 2018 by Gang Zhang and Daniele Mortari. Second-order integral-form Gauss's variational equations (GVEs) under impulsive control are derived for both nonsingular orbital elements and classical orbital elements. These equations are used to estimate the changes of the orbital elements under assigned impulsive vector. These GVEs are obtained by solving the second-order partial derivatives of orbital elements with respect to velocity vector. In addition, using analytical series approximation in the second-order GVEs, the required impulsive control is obtained for specified orbital-element variations. Based on the proposed second-order GVEs, coplanar two-impulse maneuver problems are solved to perform corrections of three and four orbital elements, respectively. Compared with the classical linear GVEs, the proposed second-order GVEs are more accurate to estimate the orbital-element variations and to solve for the required impulsive control. Several numerical examples are provided to validate the accuracy gain of the second-order GVEs.

authors

• Mortari, Daniele

published proceedings

• JOURNAL OF GUIDANCE CONTROL AND DYNAMICS

author list (cited authors)

• Zhang, G., & Mortari, D.

citation count

• 7

complete list of authors

• Zhang, Gang||Mortari, Daniele

publication date

• February 2019

publisher

• American Institute of Aeronautics and Astronautics (AIAA)  Publisher

published in

• Journal of Guidance, Control, and Dynamics  Journal

keywords

• 40 Engineering
• 4006 Communications Engineering

Digital Object Identifier (DOI)

• 10.2514/1.G003607

start page

• 284

end page

• 302

volume

• 42

issue

• 2

URL

• http://dx.doi.org/10.2514/1.g003607