Plotting particles positions over time
<p>I have drawn one position(x,y,z) of N particles in an enclosed volume.</p>

<pre><code>x[i] = random.uniform(a,b) ...
</code></pre>

<p>I also found the constant velocity(vx,vy,vz) of the N particles.</p>

<pre><code>vx[i] = random.gauss(mean,sigma) ...
</code></pre>

<p>Now I want to find the position of the N(=100) particles over time. I used the Euler-Cromer method to this.</p>

<pre><code>delta_t = linspace(0,2,n-1) 
n = 1000
v[0] = vx;...
r[0] = x;...

for i in range(n-1):
    v[i+1,:] = v[i,:]
    r[i+1,:] = r[i,:] + delta_t*v[i+1,:]
    t[i+1] = t[i] + delta_t
</code></pre>

<p>But I want to find the position over time for every particle. How can I do this? Also, how do I plot the particles position over time in 3D?</p>

<p>To find the position of the particles at a given time you can use the following code:</p>

<pre><code>import numpy as np

# assign random positions in the box 0,0,0 to 1,1,1
x = np.random.random((100,3))
# assign random velocities in the range around 0
v = np.random.normal(size=(100,3))

# define function to project the position in time according to
# laws of motion.  x(t) = x_0 + v_0 * t
def position(x_0, v_0, t):
    return x_0 + v_0*t

# get new position at time = 3.2
position(x, v, 3.2)
</code></pre>

python simulation particles