Second-Order Integral-Form Gauss's Variational Equations Under Impulsive Control
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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.
JOURNAL OF GUIDANCE CONTROL AND DYNAMICS
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Zhang, Gang||Mortari, Daniele