## 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.