Mission Design for the CubeSat OUFTI-1

CHAPTER 7.ATTITUDE CONTROL SYSTEMwhere I GC and I P are respectively the inertia moment respect to an axispassing through the gravity center and the one respect to an axis parallel to theprevious one and passing through the point P; d id the distance between thetwo axis.So the moments of inertia of the cube of uniform density respect to thegravity center of the satellite are:I x,cube = I y,cube = I z,cube = m unifl 2 (+ m unif 0.03 2 + 0.03 2) = 1.47 · 10 −3 Kgm 2 (7.3)6Then, the moment of inertia of the mass M respect to the gravity centerare:I x,M = I y,M = I z,M = M ( 0.03 2 + 0.03 2) = 7.16 · 10 −4 Kgm 2 (7.4)If we call ˆ3 the longitudinal axis of each antenna, its moments of inertiarespect to its extremities are:I long = I 1,long = I 2,long = m longl 2 long3= 3.32 · 10 −4 Kgm 2I short = I 1,short = I 2,short = m shortlshort2 = 1.39 · 10 −5 Kgm 2 (7.5)3I 3,long∼ = I3,short∼ = 0With the y-axis directed as the longer antennas and the z-axis as the shorter,we can now have the antennas moments of inertia respect to gravity center:(7.6)I x,ant(=I long + m long 0.02 2 + 0.03 3) (+ I long + m long 0.02 2 + 0.07 3) +(+I short + m short 0.02 2 + 0.03 3) (+ I short + m short 0.02 2 + 0.07 3) =I y,ant=7.28 · 10 −4 Kgm 2(=m long 0.02 2 + 0.02 3) (+ m long 0.02 2 + 0.02 3) +(+I short + m short 0.02 2 + 0.03 3) (+ I short + m short 0.02 2 + 0.07 3) ==6.93 · 10 −4 Kgm 2I z,ant=4.38 · 10 −5 Kgm 2(=I long + m long 0.02 2 + 0.03 3) (+ I long + m long 0.02 2 + 0.07 3) +(+m short 0.02 2 + 0.02 3) (+ m short 0.02 2 + 0.02 3) =Hence, the total moment of inertia are:Galli Stefania 65 University of Liège