(a) Prove that, for all ,,, is a proper orthogonal matrix. (b) Write down a formula for...
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(a) Prove that, for all θ,ϕ,ψ,
is a proper orthogonal matrix.
(b) Write down a formula for Q−1. Remark. It can be shown that every proper orthogonal matrix can be parameterized in this manner; θ,ϕ,ψ are known as the Euler angles, and play an important role in applications in mechanics and geometry.
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a To prove that the given matrix is a proper orthogonal matrix we need to show that 1It is an orthog...View the full answer
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