Path: Orbit/RHSOrbit
% Computes the linearized orbit equations.
To get normalized equations with nt as the independent variable, just
set n = 1. Pass x as empty to get the state equations. If dT is entered it
will generate the discrete time equations
y = c*x[k] + d*u[k]
x[k+1] = a*x[k] + b*u[k]
otherwise
y = c*x + d*u
dx/dt = a*x + b*u
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Form:
xD = LinOrb( x, n, aD )
[a, b, c, d] = LinOrb( [], n, [], dT )
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Inputs
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x (6,1) state [dr;rtheta;z;ddr/dt;drtheta/dt;dz/dt]
n (1,1) orbit rate
aD (3,1) acceleration vector
dT (1,1) time step
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Outputs
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a (6,6) State transition matrix or (6,1) state derivative
b (6,3) Input matrix
c (3,6) Output matrix (position)
d (3,3) Feedthrough matrix
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References: Kaplan, M., Modern Spacecraft Dynamics and Control, p. 111.
Valado, D., Fundamentals of Astrodynamics and Applications,
pp. 348-51.
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