# Intergrator Verlet¶

## Overview¶

Integrating state via two step velocity-Verlet

$\begin{split}{\bf v}_i\left(t+\frac{1}{2}\Delta t\right) &=& {\bf v}_i\left(t\right) + \frac{1}{2}\frac{{\bf f}_i\left(t\right)}{m_i}\Delta t\\ {\bf r}_i\left(t+\Delta t\right) &=& {\bf r}_i\left(t\right) + {\bf v}_i\left(t+\frac{1}{2}\Delta t\right)\Delta t\\ {\bf v}_i\left(t+\Delta t\right) &=& {\bf v}_i\left(t+{\Delta t}/{2}\right)+\frac{1}{2}\frac{{\bf f}_i\left(t+\Delta t\right)}{m_i}\Delta t\end{split}$

where $${\bf r}_{i}$$ is coordinate of particle $$i$$, $${\bf v}_i$$ is velocity of particle $$i$$, $${\bf f}_i$$ is sum of all forces acting on particle $$i$$, $$m_i$$ is mass particle $$i$$, and $$\Delta t$$ is timestep size. The timestep size is set through state variable:

state.dt=0.005


## Python Member Functions¶

Constructor

IntegratorVerlet(state=...)


Arguments

state
state object.

Integrating state is done with run.

run(numTurns=...)


Arguments

numTurns
number of timestep to make.

TODO Write Output?

## Examples¶

integrater = IntegratorVerlet(state)


Setting parameters in python

state.shoutEvery=1000
state.dt=0.005


integrating system forward in time

#run 1E5 timesteps
integrater.run(100000)