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

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Concept explainers

Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related to mass distribution. For all positions of the body, the center of gravity would be a single point.

Question

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, ŵ2, ñ3} and {b₁, 62, 63} are right-handed vector bases
fixed in N-frame and B-frame, respectively. {1;} is aligned with the principal axis of inertia, where ☎₁ and
3 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) = 2ñ₁ñ₁ +2.25 ñ¿Ñ₂ +2.25 ñ³Ñ3 – 0.75 ñ¿ñ3 −0.75 3₂ (dimensionless)
Express the satellite inertia tensor about the CoM in B-frame.
Determine [BN] at time t = 0, i.c., the direction cosine matrix (DCM) that represents the
orientation of B-frame relative to N-frame.

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