Question

Derive the matrix that represents a pure rotation about the (i) y-axis , (ii) z-axis and (iii) x-axis of the reference frame with the help of diagram.

Matrices
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asked 2021-02-20
Derive the matrix that represents a pure rotation about the (i) y-axis , (ii) z-axis and (iii) x-axis of the reference frame with the help of diagram.

Answers (1)

2021-02-21
Step 1:- Introduction:-
A basic rotation also called elemental rotation is a rotation about one of the axes of a co-ordinate system.
Step 2:- Calculation:-
The Following three basic rotation matrices rotate vectors by an angle \(\theta\) about x, y, z axes , in three dimensions which codifies their alternating signs.
\(R_x(\theta)=\begin{bmatrix}1 & 0&0 \\0 & \cos\theta&-\sin\theta\\0&\sin\theta&\cos\theta \end{bmatrix}\)
\(R_y(\theta)=\begin{bmatrix}\cos\theta & 0&\sin\theta \\0 & 1&0\\-\sin\theta&0&\cos\theta \end{bmatrix}\)
\(R_z(\theta)=\begin{bmatrix}\cos\theta & -\sin\theta&0 \\\sin\theta & \cos\theta&0\\0&0&1 \end{bmatrix}\)
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