vpython_catenary_animation

#27_08_21

'''
 From:
 "Modeling a Catenary Cable as a Bunch of Masses Connected by Springs"
 in Rhett Allain's Physics Explained Channel

 tested on: Linux Mint 20.2, Geany 1.36, python 3.8.10,
 Web Epiphany, i5-7260U CPU @ 2.20GHz × 2, Iris Plus Graphics 640
 vpython version: ['7.6.1', 'jupyter']

'''

from vpython import *
import sys

def main():
    print(version)

    scene.width, scene.height = 1900, 980
    scene.align = 'left'
    scene.autoscale = False
    scene.autozoom = False
    scene.userspin = True
    scene.userzoom = True
    scene.userpan = False
    scene.resizable = False
    scene.range = 0.25

    CATENARY = 1

    HORIZONTAL = 1

    RATE = 200

    dt = 0.001

    # NUMBER OF BALLS (CHAIN LINKS)
    N = 20

    # LINEAR LENGTH OF CHAIN IN "RELAXED" STATE
    L = 0.2

    # TOTAL MASS
    M = 0.1

    # INDIVIDUAL MASS
    #mass = M/N
    mass = 0.005

    # SPRING CONSTANT
    k = 70

    # GRAVITY ACCELERATION VECTOR
    A = vec(0, -9.8, 0)

    # Fdrag = -C * momentum (p)
    C = 3.0

    if CATENARY:
        leftend = vec(-0.1, 0.1, 0)
    else:
        leftend = vec(0, 0.2, 0)

    if HORIZONTAL or CATENARY:
        ds = vec(1, 0, 0) * L/(N-1)
    else:
        ds = vec(0, -1, 0) * L/(N-1)

    # SPRING "RELAXED" LENGTH
    Srel = L/(N-1)

    # BALL RADIUS
    R = 0.004

    # CONSTRUCT THE CHAIN
    balls = []
    for i in range(N):
        balls += [sphere(pos=leftend+i*ds, radius=R, m=mass,
        color=color.white, p=vec(0,0,0), F=vec(0,0,0))]
    springs = []
    for i in range(N-1):
        springs += [cylinder(pos=leftend+i*ds, axis=ds, radius=R/6)]


    t = 0
    while t < 4:

        rate(RATE)

        # CHAIN LEFTEND
        balls[0].F = vec(0,0,0)

        # CHAIN MIDDLE
        for i in range(1, N-1):

            Fgrav = balls[i].m * A
            Fspr0 = -k*(mag(springs[i-1].axis)-Srel) * norm(springs[i-1].axis)
            Fspr1 = +k*(mag(springs[i].axis)-Srel) * norm(springs[i].axis)
            Fdrag = -C * balls[i].p

            balls[i].F = Fspr0 + Fspr1 + Fgrav + Fdrag

        # CHAIN RIGHTEND
        if CATENARY:
            balls[-1].F = vec(0,0,0)
        else:
            Fgrav = balls[-1].m * A
            Fspr0 = -k*(mag(springs[-1].axis)-Srel) * norm(springs[-1].axis)
            Fdrag = -C * balls[-1].p

            balls[-1].F = Fspr0 + Fgrav + Fdrag

        for ball in balls:
            ball.p += ball.F * dt
            ball.pos += ball.p * dt/ball.m

        for i in range(1, N):
            springs[i-1].axis = balls[i].pos - balls[i-1].pos
            springs[i-1].pos = balls[i-1].pos

        t += dt

    # PRINT FINAL LENGTH OF CHAIN
    Lnew = 0
    for i in range(1,N):
        dLnew = mag(balls[i].pos - balls[i-1].pos)
        Lnew += dLnew
    print('New Length', Lnew)


class g: ...


if __name__ == '__main__':
    sys.exit(main())