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Extra info for A bad network problem for the simplex method and other minimum cost flow algorithms

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For given rectangular satellite state vector ˙ T to compute the Keplerian elements, can be carried out as follows. ω + f is (r, r) called argument of latitude and denoted by u. ˙ 1. Using the given state vector to compute the modulus r and v (r = |r|, v = |r|); 2. 4 State Vector of the Satellite 35 RO O F 3. 14) to compute inclination i and the right ascension of ascending node Ω; 4. 32) to compute semi-major axis a, eccentricity e and average angular velocity n; 5. 46) to compute ω + f ; 6. 47) to compute ω and f ; 7.

56) turns out to be (denoted by Q) ⎤ ⎡ Pn (sin ϕ )Pn (sin ϕs ) + (2 − δ0n ) ∞ n ae ⎣ n ⎦. (n − k)! Q = Gσ Hds ∑ n+1 Pnk (sin ϕ )Pnk (sin ϕs ) cos k(λs − λ ) ×∑ r n=0 k=0 (n + k)! 57) EC The direct ocean tide potential is then the integration of Q/ds over the ocean (denoted by O), including the potential of the deformation of the ocean loading. The ocean tide potential is then ⎤ ⎡ Pn (sin ϕ )Pn (sin ϕs ) + (2 − δ0n ) ane ⎣ ⎦ ds, n (n − k)! Gσ H ∑ (1 + kn ) n+1 r Pnk (sin ϕ )Pnk (sin ϕs ) cos k(λs − λ ) ×∑ n=0 k=0 (n + k)!

5 Mean anomaly of satellite 32 3 Keplerian Orbits F projection of the satellite S on the circle with a radius of a (semi-major axis of the ellipse). The distance between the geometric centre O of the ellipse and the geocentre O is ae. 33) RO O y = r sin f = b sin E = a 1 − e2 sin E, where the second equation can be obtained by substituting the first into the standard ellipse equation (x2 /a2 + y2 /b2 = 1) and omitting the small terms that contain e (for the satellite, generally, e << 1), where b is the semi-minor axis of the ellipse.

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A bad network problem for the simplex method and other minimum cost flow algorithms by Zadeh N.


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