Matplotlib Animation: Passing variables through FuncAnimation

You can use functools.partial or a lambda function. Let's say you change your code so ball_1 and ball_1_plt are not global anymore, but arguments to DEM. Then you call it like this:

from functools import partial
animation_run = FuncAnimation(
    fig,
    func=partial(DEM, ball_1=ball_1, ball_1_plot=ball_1_plot),
    frames=[10,20],
    interval=10
)

The references would persist between calls, so it should work, but you can not assign them within DEM. In other words, replace this:

ball_1 = [[acc_x,vel_x,pos_x],[acc_y,vel_y,pos_y]]

by this:

ball_1[0] = [acc_x,vel_x,pos_x]
ball_1[1] = [acc_y,vel_y,pos_y]

Explanation

The reason is the same reason your code is failing right now. When you assign ball_1, a new variable is bound. This variable is local. Your current code would run if you add the statement global ball_1 at the top of the function. However, it is better to not use globals, but pass arguments as you suggest in your question.

This is your code without any globals, moving your top-level code into a function, and passing arguments to DEM:

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation


def DEM(step, ball_1, ball_1_plot):
    TS = step/10

    # Ball_1
    # Contact
    grav = -9.81

    # Acceleration
    acc_x = 0
    acc_y = grav

    # Velocity
    vel_x = ball_1[0][1] + acc_x*TS
    vel_y = ball_1[1][1] + acc_y*TS

    # Position
    pos_x = vel_x * TS + 0.5 * acc_x * TS * TS  + ball_1[0][2]
    pos_y = vel_y * TS + 0.5 * acc_y * TS * TS  + ball_1[1][2]

    # Update
    ball_1[0] = [acc_x,vel_x,pos_x]
    ball_1[1] = [acc_y,vel_y,pos_y]

    # Update animation
    ball_1_plot.set_xdata(ball_1[0][2])
    ball_1_plot.set_xdata(ball_1[1][2])

    return ball_1_plot,

def main():
    from functools import partial

    fig, ax = plt.subplots()
    ax.set_xlim(0,100)
    ax.set_ylim(0,100)

    #         acc,vel,disp (x,y)
    ball_1 = [[0,0,40],[0,0,100]]
    ball_1_plot, = ax.plot(ball_1[0][2],ball_1[1][2], "o")

    animation_run = FuncAnimation(fig,func=partial(DEM, ball_1=ball_1, ball_1_plot=ball_1_plot), frames=[10,20], interval=10)
    plt.show()


if __name__ == '__main__':
    main()