Appendix_D - Appendix D Page 1 of 101 9:07 AM Appendix D...

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Appendix D Page 1 of 101 10/27/09 9:07 AM Appendix D MATLAB algorithms Appendix Outline D.1 Introduction D.2 Algorithm 1.1: numerical integration of a system of first order differential equations by choice of Runge-Kutta methods RK1, RK2, RK3 or RK4 D.3 Algorithm 1.2: numerical integration of a system of first order differential equations by Heun’s predictor-corrector method. D.4 Algorithm 1.3: numerical integration of a system of first order differential equations by the Runge-Kutta-Fehlberg 4(5) method with adaptive step size control. D.5 Algorithm 2.1: numerical solution for the motion of two bodies relative to an inertial frame. D.6 Algorithm 2.2: numerical solution for the motion m 2 of relative to m 1 . D.7 Calculation of the Lagrange coefficients f and g and their time derivatives in terms of change in true anomaly. D.8 Algorithm 2.3: calculation of the state vector given the initial state vector and the change in true anomaly. D.9 Algorithm 2.4: find the root of a function using the bisection method. D.10 MATLAB solution of Example 2.18 D.11 Algorithm 3.1: solution of Kepler’s equation by Newton’s method D.12 Algorithm 3.2: solution of Kepler’s equation for the hyperbola using Newton’s method D.13 Calculation of the Stumpff functions S ( z ) and C ( z ) D.14 Algorithm 3.3: solution of the universal Kepler’s equation using Newton’s method D.15 Calculation of the Lagrange coefficients f and g and their time derivatives in terms of change in universal anomaly D.16 Algorithm 3.4: calculation of the state vector given the initial state vector and the time lapse Δ t D.17 Algorithm 4.1: obtain right ascension and declination from the position vector
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Appendix D Page 2 of 101 10/27/09 9:07 AM D.18 Algorithm 4.2: calculation of the orbital elements from the state vector D.19 Calculation of tan 1 yx () to lie in the range 0 to 360°. D.20 Algorithm 4.3: obtain the classical Euler angle sequence from a DCM. D.21 Algorithm 4.4: obtain the yaw, pitch and roll angles from a DCM. D.22 Algorithm 4.5: calculation of the state vector from the orbital elements D.23 Algorithm 4.6: calculate the ground track of a satellite from its orbital elements. D.24 Algorithm 5.1: Gibbs method of preliminary orbit determination D.25 Algorithm 5.2: solution of Lambert’s problem D.26 Calculation of Julian day number at 0 hr UT D.27 Algorithm 5.3: calculation of local sidereal time D.28 Algorithm 5.4: calculation of the state vector from measurements of range, angular position and their rates D.29 Algorithms 5.5 and 5.6: Gauss method of preliminary orbit determination with iterative improvement D.30 Calculate the state vector at the end of a finite-time, constant thrust delta-v maneuver. D.31 Algorithm 7.1: Find the position, velocity and acceleration of B relative to A ’s co-moving frame. D.32 Plot the position of one spacecraft relative to another.
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Appendix_D - Appendix D Page 1 of 101 9:07 AM Appendix D...

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