Continuum mechanics/Kinematics Test

1. $\{\xi ^{1},\xi ^{2},\xi ^{3}\}$ — Lagrangian coordinates, $\{x,y,z\}$ — Eulerian coordinates.

Law of medium motion is given:

$x=\xi ^{1}+(\xi ^{1}+\xi ^{2})\ln(1+t)$
$y=\xi ^{2}+(\xi ^{1}-\xi ^{2})\ln(1+t)$
$z=\xi ^{3}+(\xi ^{1}+\xi ^{2})\ln(1+t)$

Find components of velocity and acceleration as functions of Lagrangian and Eulerian variables.