A closer look: Velocity Verlet Algorithm
We designed a dynamical simulation to compute the particle trajectories as a function of time. The simulation utilizes the Velocity Verlet algorithm, which calculates positions and velocities of particles via Taylor expansion. Because the Newton’s equation of motion is second order in relative position (r), the initial condition needs to specify both particle position and velocity at time 0.
The model makes use of the following equations:
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$$
{{x(t + \Delta t) }} = {{ x(t) + v(t)\Delta t + (1/2)a(t)\Delta t^2 }}
$$
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$$
{{v(t + \Delta t/2) }} = {{ v(t) + (1/2)a(t)\Delta t }}
$$
with the given time step and initial value conditions.
The whole procedure can be summarized in following steps:
