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7.4 Exercises

Gauss Dynamics:
Write a Gaussian MD program to simulate the following system:
3 particles without pairwise interaction are moving in a one-dimensional harmonic potential. The sum of their kinetic energies is kept constant. Draw the $x,\dot{x}$ trajectory of the first particle. Use Runge-Kutta.

Nosé-Hoover thermostat:
The equations of motion of the Nosé oscillator with $k=m=E_{0}=1$ are
$\displaystyle \dot{x}$ $\textstyle =$ $\displaystyle v$ (7.23)
$\displaystyle \dot{v}$ $\textstyle =$ $\displaystyle -x-\zeta   v$ (7.24)
$\displaystyle \dot{\zeta}$ $\textstyle =$ $\displaystyle \frac{1}{Q}  \left[ v^{2}-2\right]$ (7.25)

Integrate this set of equations, using Runge-Kutta, and draw the $x,v$ trajectory.

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F. J. Vesely / University of Vienna