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 )
def arctg(x): return np.degrees( np.arctan(x) )
def sins(x):  return round( np.sin( np.radians(x) )**2, 10 )
def asin(x):  return np.degrees( np.arcsin(x) )
#}}}
def sqrt(x): return x**(1./2)
# Plot setup {{{
from matplotlib import pyplot as plt
from matplotlib import rc, rcParams
rcParams['font.size'] = 20.
rcParams['text.usetex'] = True
#rc('text.latex', preamble=r'\usepackage{esvect}')
rcParams['font.sans-serif'] = ['Computer Modern']
rc('text.latex', preamble=r'\usepackage[T2A]{fontenc} \usepackage[utf8]{inputenc} \usepackage{bm}')
#rc('text.latex', preamble=r'\usepackage[utf8]{inputenc}')

rc('axes', linewidth=1.2)
rc('xtick.major', size=4, width=1.1)
rc('ytick.major', size=4, width=1.1)
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, 1.5, 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)

    # Add mu=... to the legend
    ax.plot([], [], ' ', label='$\\mu={}$'.format("{:.2f}".format(mu) ) )


    # 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)

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

    #plt.show()
    # convert -delay 0.01 -loop 0 *.pdf ftr_a_mu.gif