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The inertia matrix for the main body, B, of a spacecraft is [𝐼𝐡] 2000 200 0 200 1500 0 0 0 2200𝑠𝐼 βˆ’ 𝑓𝑑2 Where is measured relative to B's c.m. and vector basis 𝐛𝑖, which is fixed in B. B weighs 1200 lbs. A second body, C, is attached to B, as shown below. R = vector from B's c.m. to center of the base of C = 0𝐛1 + 2𝐛2 + 1𝐛3 ft C is a homogeneous, 322 lb box with sides aligned with 𝐛𝑖 a) What is the location of the system (B + C) center of mass relative to the B's c.m.? Express the answer as a vector from B's c.m. to the system's c.m. in the 𝐛𝑖 basis in feet. b) Define the inertia matrix for C relative to the system c.m. and referred to the 𝐛𝑖 basis in 𝑠𝑠 βˆ’ 𝑓𝑑2. (c) Find the inertia matrix for the system (B + C) relative to the system's c.m. and referred to 𝐛𝑖 . Indicate all equations used. Define all 9 elements of the inertia matrix in 𝑠𝐼 βˆ’ 𝑓𝑑2

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