Mission Design for the CubeSat OUFTI-1

CHAPTER 8.POWER SYSTEMFigure 8.2: Sun rays direction on the ecliptic plane⎧⎨⎩⎫ ⎡x eq ⎬y eq⎭ = ⎣z eq1 0 00 cos (i eq ) sin (i eq )0 −sin (i eq ) cos (i eq )⎤ ⎧⎨⎦⎩⎫x ecl ⎬y ecl⎭ = R 1z ecl(8.2)One we have our vector expressed in the equatorial plane, we pass into afirst intermediate reference by turning of the right ascension of ascending nodeΩ about the z eq = z ′ axis with the rotation matrix R 2 :⎧⎨⎩⎫ ⎡x ′ ⎬y ′z ′ ⎭ = ⎣cos (Ω) sin (Ω) 0−sin (Ω) cos (Ω) 00 0 1⎤ ⎧⎨⎦⎩⎫x eq ⎬y eq⎭ = R 2z eq⎧⎨⎩⎧⎨⎩x ecly eclz ecl⎫⎬⎭x eqy eqz eq⎫⎬⎭ (8.3)Then we can consider the orbit inclination i for a rotation about the x ′ = x ′′axis thanks to the rotation matrix R 3 and passing into a second intermediatereference:⎧⎨⎩⎫ ⎡x ′′ ⎬y ′′z ′′ ⎭ = ⎣1 0 00 cos (i) sin (i)0 −sin (i) cos (i)⎤ ⎧⎨⎦⎩⎫x ′ ⎬y ′z ′ ⎭ = R 3⎧⎨⎩x ′y ′z ′ ⎫⎬⎭(8.4)This second reference system is on the orbit plane but the abscissas axisisn’t oriented to the perigee. We consider therefore the argument of perigee byrotating about the z ′′ = z orb with the matrix R 4 :⎧⎨⎩⎫ ⎡x orb ⎬y orb⎭ = ⎣z orbcos (ω) sin (ω) 0−sin (ω) cos (ω) 00 0 1⎤ ⎧⎨⎦⎩⎫x ′′ ⎬y ′′z ′′ ⎭ = R 4⎧⎨⎩x ′′y ′′z ′′ ⎫⎬⎭ (8.5)Galli Stefania 75 University of Liège