glasskerfu

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.

Alannej

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.
${R}_{x}\left(\theta \right)=\left[\begin{array}{ccc}1& 0& 0\\ 0& \mathrm{cos}\theta & -\mathrm{sin}\theta \\ 0& \mathrm{sin}\theta & \mathrm{cos}\theta \end{array}\right]$
${R}_{y}\left(\theta \right)=\left[\begin{array}{ccc}\mathrm{cos}\theta & 0& \mathrm{sin}\theta \\ 0& 1& 0\\ -\mathrm{sin}\theta & 0& \mathrm{cos}\theta \end{array}\right]$
${R}_{z}\left(\theta \right)=\left[\begin{array}{ccc}\mathrm{cos}\theta & -\mathrm{sin}\theta & 0\\ \mathrm{sin}\theta & \mathrm{cos}\theta & 0\\ 0& 0& 1\end{array}\right]$

Jeffrey Jordon