A example of MD simulation

This is a homework of computational nanomechanics. The basic requirement is to use the 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.

(more…)