A example of MD simulation

This is a homework of computational nano mechanics. The basic requirement is to use Lagrangian function to describe the motion of particles. In homework, it requires 5 particles. As an enhancement, I rewrote the code with Qt and use GNU Scientific Library(GSL) to finish the task.

Concept

The Lagrangian equation of motion describe the particle motion with energy method, the equation is:

\[ \displaystyle \frac{d}{dt}\frac{\partial L}{\partial \dot{x}_k}-\frac{\partial L}{\partial x_k}=0\]

\( L\) is the Lagrangian function of the system, \( k\) denotes the degree of freedom.

\[ \displaystyle L = T – U\]

\( T\) is the kinetic energy and \( U\) is the potential energy.

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