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.