问题描述:

I have drawn one position(x,y,z) of N particles in an enclosed volume.

`x[i] = random.uniform(a,b) ...`

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

`vx[i] = random.gauss(mean,sigma) ...`

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

`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

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?

To find the position of the particles at a given time you can use the following 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)
```