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

Adding the integrator

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)