Classical Dynamics of Particles and Systems · Problem 1-15

Newtonian Mechanics—Single Particle — Marion & Thornton

Physics — Mechanics · orthogonal-transformations

Problem

Find the values of

\alpha

needed to make the following transformation orthogonal.

\begin{pmatrix} 1 & 0 & 0 \\ 0 & \alpha & -\alpha \\ 0 & \alpha & \alpha \end{pmatrix}