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.