...
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:
| Latex |
|---|
\\
The following equations are used:
\\
{latex}
\large
$$
{{x(t + \Delta t) }} = {{ x(t) + v(t)\Delta t + (1/2)a(t)\Delta t^2 }}
$$
|
| Latex |
|---|
{latex} \\ {latex} \large $$ {{v(t + \Delta t/2) }} = {{ v(t) + (1/2)a(t)\Delta t }} $$ {latex} \\ !fig2.png|align=center! |
with the given time step and initial value conditions.
The whole procedure can be summarized in following steps:
