...
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:
| Wiki Markup |
|---|
\\ {latex} \large $$ {{x(t + \Delta t) }} = {{ x(t) + v(t)\Delta t + (1/2)a(t)\Delta t^2 }} $$ {latex} \\ |
| Wiki Markup |
|---|
{latex}
\large
$$
{{v(t + \Delta t/2) }} = {{ v(t) + (1/2)a(t)\Delta t }}
$$
{latex}
\\
|
with
...
the
...
given
...
time
...
step
...
and
...
initial
...
value
...
conditions.
...
The whole procedure can be summarized in following steps:
