Chapter 2, Problem 113CE

Derive the following expressions for the components of acceleration of an object, $a_x^{\text{'}}$ and $a_y^{\text{'}}$ , in frame $S\text{'}$ in terms of its components of acceleration and velocity in frame S.

$a_x^{\text{'}}=\frac{a_x}{{\gamma }_v^3{\left(1-\frac{u_{x}v}{c^2}\right)}^3}$

$a_y^{\text{'}}=\frac{a_y}{{\gamma }_v^2{\left(1-\frac{u_{x}v}{c^2}\right)}^2}+\frac{a_x\frac{u_{y}v}{c^2}}{{\gamma }_v^2{\left(1-\frac{u_{x}v}{c^2}\right)}^3}$