Consider a satellite moving in a torque-free environment. The inertial frame and satellite body-fixed frame are represented by N-frame and B-frame, where {1,2,3} and {b1, 62, 63} are right-handed vector bases fixed in N-frame and B-frame, respectively. {b;} is aligned with the principal axis of inertia, where b₁ and 63 are associated with the minimum and maximum moments of inertia, respectively. Denote the satellite angular velocity by w = wib; and the inertia tensor about the CoM by Ic. Suppose that I at time t = 0 is given by: Ic(t = 0) = 2n₁n₁ +2.25 n₂n₂ +2.25ñ33 -0.75 m₂3 -0.75 n3n2 (dimensionless) Express the satellite inertia tensor about the CoM in B-frame. Determine [BN] at time t = 0, i.e., the direction cosine matrix (DCM) that represents the orientation of B-frame relative to N-frame.

Consider a satellite moving in a torque-free environment. The inertial frame and satellite body-fixed frame are represented by N-frame and B-frame, where {1,2,3} and {b1, 62, 63} are right-handed vector bases fixed in N-frame and B-frame, respectively. {b;} is aligned with the principal axis of inertia, where b₁ and 63 are associated with the minimum and maximum moments of inertia, respectively. Denote the satellite angular velocity by w = wib; and the inertia tensor about the CoM by Ic. Suppose that I at time t = 0 is given by: Ic(t = 0) = 2n₁n₁ +2.25 n₂n₂ +2.25ñ33 -0.75 m₂3 -0.75 n3n2 (dimensionless) Express the satellite inertia tensor about the CoM in B-frame. Determine [BN] at time t = 0, i.e., the direction cosine matrix (DCM) that represents the orientation of B-frame relative to N-frame.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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