Plot friction force vs. angle

ftr-a-mu.py

import numpy as np

# Triginometry {{{
def cos(x):   return round( np.cos( np.radians(x) ), 10 )
def sin(x):   return round( np.sin( np.radians(x) ), 10 )
def tg(x):    return round( np.tan( np.radians(x) ), 10 )
#}}}

# Plot setup {{{
from matplotlib import pyplot as plt
from matplotlib import rc, rcParams
rcParams['font.size'] = 20.
rc('axes', linewidth=1.2)
rc('xtick.major', size=4, width=1.1)
rc('ytick.major', size=4, width=1.1)
plt.rcParams.update({
    "text.usetex": False,
    "mathtext.fontset": "custom",
    "mathtext.it": "STIX Two Text:italic",
    "mathtext.rm": "STIX Two Text",
    "mathtext.sf": "STIX Two Text",
    "font.sans-serif": "STIX Two Text",
})
fig, ax = plt.subplots(figsize=(8,8))
fig.subplots_adjust(left=.15, bottom=.15, right=.95, top=.83)
#}}}

# Initial parameters (SI units)
m  = 1
g  = 10
mu = tg(35)
alpha = np.linspace(0, 90, 1500)
mus = np.linspace(0, 1.0, 500)

for mu in mus:
    Ftr=[]

    for a in alpha:
        if mu > tg(a):
            Ftr = np.append(Ftr, m*g*sin(a))
        else: 
            Ftr = np.append(Ftr, mu*m*g*cos(a))

    ax.set_xlim([0,90])
    ax.set_ylim([0,10.5])
    ax.set_xlabel('$\\alpha$ [$^{\\circ}$]')
    #ax.set_ylabel('$F_\\textrm{тр}$ [\\textrm{Н}]')
    #ax.plot(alpha, Ftr, lw=2.5, label='$F_\\textrm{тр}$', zorder=4)
    ax.set_ylabel(r'$F_{\rm тр}$ [Н]')
    ax.plot(alpha, Ftr, lw=2.5, label=r'$F_{\rm тр}$', zorder=4)

    # Add mu=... to the legend
    #ax.plot([], [], ' ', label='$\\mu={}$'.format("{:.2f}".format(mu)).replace('.', '{,}') )
    ax.plot([], [], ' ', label='$~$' )
    ax.text(23, 11.281, '$\\mu={}$'.format("{:.2f}".format(mu)).replace('.', '{,}'), zorder=99 )


    # Plot full mgsina
    Ftr=[]
    for a in alpha:
        Ftr = np.append(Ftr, m*g*sin(a))
    ax.plot(alpha, Ftr, ':', label='$mg\\sin{\\alpha}$', c='orange')

    # Plot full μmgcosa
    Ftr=[]
    for a in alpha:
        Ftr = np.append(Ftr, mu*m*g*cos(a))
    ax.plot(alpha, Ftr, '--', label='$\\mu mg\\cos{\\alpha}$', c='green')


    ax.set_axisbelow(True)
    ax.grid()

    ax.legend(loc='upper center', bbox_to_anchor=(0.5, 1.23), shadow=True, ncol=2, handlelength=1.5)

    plt.savefig('plots/' + str(mu)+'.png', dpi=303, bbox_inches='tight')
    plt.cla()

## Then create video using ffmpeg:
# ffmpeg -framerate 30 -pattern_type glob -i "*.png" -c:v libx264 -r 30 -pix_fmt yuv420p output.mp4