Keplerian State Transition Matrix 1.0

Phi = keplerSTM(x0,dt,mu) will return the state transition matrix Phi for a set of objects described by initial positions and velocities (x0) with gravitational parameters mu, propogated along Keplerian orbits for time dt. The positions and velocities at time dt is then given by Phi*x0. x0 must be a row vector of length 6n where n is the number of planets. For each planet, x0 must include the 3 position and 3 velocity values in the order [r1,r2,r3,v1,v2,v3].' These positions and velocities are measured in a cartesian coordinate system with the central object (i.e. star) at the origin. For multiple planets, simply stack several of these vectors on top of each other. mu must contain n values equal to G(m+ms) where G is the gravitational constant, m is the mass of the orbiting object, and ms is the mass of the central object. dt is a scalar value of time to propogate. NOTE: All units should be consistent. If the positions are in AU and velocities are in AU/day, then dt must be in days, and mu must be in AU^3/day^2. This is calculated using the algorithm described in Shepperd, 1984 which employs Goodyear's universal variables and solves the Kepler problem using continued fractions. Example: %propogate a planet 10 days along its orbit: x0 = [-0.8684, -0.6637, 0.7207, 0.0039, 0.0056, 0.0120].'; x1 = keplerSTM(x0,10,2.6935e-04)*x0;

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	And Ms,  And Mu,  Are In,  At The,  Au And,  Auday,  Be In,  Calculated,  Cartesian Coordinate,  Central Object,  Consistent,  Continued Fractions,  Day,  Keplerian,  Measured,  Phix,  Solves,  Time,  Velocities
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