2. A frame {B} is located initially coincident with a frame {A}. VWe rotate {B} about2B by 60 degrees, and then we rotate the resulting frame about XB by 30 degrees.Give the rotation matrix that will change the description of vectors from BP to ^P.

Answered: 2. A frame {B} is located initially…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. A frame {B} is located initially coincident with a frame {A}. VWe rotate {B} about
2B by 60 degrees, and then we rotate the resulting frame about XB by 30 degrees.
Give the rotation matrix that will change the description of vectors from BP to ^P.

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$Given that frame is initially coincident with frame (A) Let (M) be the intermediate position when frame (B) is rotated about X - axis by 90 ° and final position of frame (B) say' P' obtained by rotation of frame (B) from (M) by 30 ° and its y - axis (assume 3 \times 3 same) {}_{B}^{A}P = {}_{M}^{A}R - {}_{B}^{M}R = {}_{M}^{A}R_{(60 ° xaxis)} . {}_{B}^{M}R_{(30 y ‐ axis)} = [\begin{matrix} 1 & 0 & 0 \\ 0 & \cos 60 ° & - \sin 60 ° \\ 0 & \sin 60 ° & \cos 60 ° \end{matrix}] . [\begin{matrix} \cos 30 ° & 0 & \sin 30 ° \\ 0 & 1 & 0 \\ - \sin 30 ° & 0 & \cos 30 ° \end{matrix}] = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 / 2 & \frac{- \sqrt{2}}{2} \\ 0 & \frac{\sqrt{3}}{2} & \frac{1}{2} \end{matrix}] [\begin{matrix} \frac{\sqrt{3}}{2} & 0 & \frac{1}{2} \\ 0 & 1 & 0 \\ \frac{- 1}{2} & 0 & \frac{\sqrt{3}}{2} \end{matrix}]$

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