Question

Problem E4 The orientation of a frame B: \{\hat{b}_1,\hat{b}_2,\hat{b}_3\} relative to frame N: \{\hat{n}_1,\hat{n}_2,\hat{n}_3\} is shown below. (Note that the directions of the two dashed lines are opposite to the \hat{n}_1, \hat{n}_2 directions.) a) Find the direction cosine matrix (DCM) [B/N] representing the rotation from the N frame to the B frame. b) Write the three body-frame unit vectors \hat{b}_1, \hat{b}_2, \hat{b}_3 as well as vector \^{B}v = (1,1,1) resolved into the N frame (i.e. give the components of \^{N}\hat{b}_1, \^{N}\hat{b}_2, \^{N}\hat{b}_3 and \^{N}v). c) If frame F: \{\hat{f}_1,\hat{f}_2,\hat{f}_3\} is defined by a 3-1-3 Euler angle sequence (\psi, \theta, \phi) = (140,90,0) deg from frame N, what is the DCM for the relative orientation of frame F with respect to frame B?

          Problem E4
The orientation of a frame B: \{\hat{b}_1,\hat{b}_2,\hat{b}_3\} relative to frame N: \{\hat{n}_1,\hat{n}_2,\hat{n}_3\} is shown below. (Note that
the directions of the two dashed lines are opposite to the \hat{n}_1, \hat{n}_2 directions.)
a) Find the direction cosine matrix (DCM) [B/N] representing the rotation from the N frame to the B
frame.
b) Write the three body-frame unit vectors \hat{b}_1, \hat{b}_2, \hat{b}_3 as well as vector \^{B}v = (1,1,1) resolved into the N
frame (i.e. give the components of \^{N}\hat{b}_1, \^{N}\hat{b}_2, \^{N}\hat{b}_3 and \^{N}v).
c) If frame F: \{\hat{f}_1,\hat{f}_2,\hat{f}_3\} is defined by a 3-1-3 Euler angle sequence (\psi, \theta, \phi) = (140,90,0) deg from
frame N, what is the DCM for the relative orientation of frame F with respect to frame B?

Problem E4
The orientation of a frame B: {b̂1,b̂2,b̂3} relative to frame N: {n̂1,n̂2,n̂3} is shown below. (Note that
the directions of the two dashed lines are opposite to the n̂1, n̂2 directions.)
a) Find the direction cosine matrix (DCM) [B/N] representing the rotation from the N frame to the B
frame.
b) Write the three body-frame unit vectors b̂1, b̂2, b̂3 as well as vector B̂v = (1,1,1) resolved into the N
frame (i.e. give the components of N̂b̂1, N̂b̂2, N̂b̂3 and N̂v).
c) If frame F: {f̂1,f̂2,f̂3} is defined by a 3-1-3 Euler angle sequence (ψ, θ, ϕ) = (140,90,0) deg from
frame N, what is the DCM for the relative orientation of frame F with respect to frame B?

Added by Travis M.

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