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Mathematical Models for Small Satellite Attitude Dynamics and Kinematics
Published in Chingiz Hajiyev, Halil Ersin Soken, Fault Tolerant Attitude Estimation for Small Satellites, 2020
Chingiz Hajiyev, Halil Ersin Soken
Here u is the argument of latitude, which is simply sum of true anomaly (υ) and argument of perigee (ω) as u = ω + υ, i is the inclination angle and Ω is the right ascension of ascending node.
Adaptive kriging-assisted optimization of low-thrust many-revolution transfers to geostationary Earth orbit
Published in Engineering Optimization, 2021
Renhe Shi, Teng Long, Hexi Baoyin, Nianhui Ye, Zhao Wei
The minimum-time low-thrust GEO transfer optimization problem can be generally formulated in Equation (1): where x and u are the state and control variables, respectively; J is the performance index (i.e. the total transfer time ); are the motion equations; and presents the terminal state constraints. The motion equations are established in terms of classical orbital elements combined with the mass–flow rate equation, as shown in Equation (2) (Yang 2001): where n, E and f are the orbit mean motion, eccentric anomaly and true anomaly, respectively; p = a(1− e2) is the latus rectum; u = + f is the argument of latitude; Isp is the specific impulse of the EP system; g0 is the gravitational acceleration at sea level; m is the mass of the spacecraft; T0 is the maximum thrust of the EP system; and F = [FR, FT, FN] are the acceleration components expressed in the RTN coordinate system that is defined in the Appendix. F consists of two parts, i.e. the thrust accelerations provided by the thrusters and the Earth’s oblateness perturbations. In this work, the disturbances caused by the first four zonal harmonics of non-spherical gravitational potential are taken into account (Ghosh et al. 2015). Since the EP system is incapable of operating during eclipses because the solar arrays cannot generate power in the shadow of the Earth, an Earth conical shadow model (Yang 2001) is employed to address the eclipse problem during orbital transfer. It is assumed that T0 = 0 when the satellite enters the shadow of the Earth.