Animation F_friction(t) plot for phys.pro/problems/237/

237-gif.py

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rc, rcParams

from matplotlib.ticker import FuncFormatter
from matplotlib.ticker import MultipleLocator


# Set parameters
m = 2  # kg
R = 1  # m
g = 10 # m/s²
a = np.radians(30) # deg

T = 5 # s
w = 2*np.pi / T # rad/s

t = np.linspace(0, 2*T, 1000)
R_values = np.linspace(0, 3.1*g*np.sin(a)/w**2, 400)

for R in R_values:

    # Plot setup {{{
    lw = 2
    k=1.4
    rcParams['font.size'] = 24
    rcParams['text.usetex'] = True
    rcParams['font.sans-serif'] = ['Computer Modern']
    rc('text.latex', preamble=r'\usepackage[T2A]{fontenc} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{bm}')

    rc('axes', linewidth=lw)
    rc('xtick.major', size=4, width=lw)
    rc('ytick.major', size=4, width=lw)
    fig, ax = plt.subplots(figsize=(12,7))
    fig.subplots_adjust(left=.20, bottom=.13, right=.90, top=.68)

    # Set comma as a decimal separator (bad)
    import locale
    locale.setlocale(locale.LC_NUMERIC, 'ru_RU')
    rcParams['axes.formatter.use_locale'] = True
    def format_decimal(value, tick_number):
        value = round(value, 2) # Fixes 0,60000000000001 instead of 0,6
        return '$' + str(value).replace('.', '{,}') + '$'
    #ax.yaxis.set_major_formatter(FuncFormatter(format_decimal))
    #ax.xaxis.set_major_formatter(FuncFormatter(format_decimal))
    #}}}

    F = m * g * np.sqrt((w**2 * R/g)**2 + 2 * w**2 * R * np.sin(a)/g * np.cos(w*t) + np.sin(a)**2)
    ax.plot(t, F, label=r'$F_\textrm{тр}(t) = mg \sqrt{\left(\dfrac{\omega^2R}{g}\right)^{\kern-9pt 2} + \dfrac{2\omega^2R\sin\alpha}{g} \cdot \cos\omega t + \sin^2\alpha}$', lw=lw*1.5)
    print( round(R,3) )
    plt.figtext(0.27, 0.73, r'$m\omega^2R = {}\cdot mg\sin\alpha$'.format('{:0.2f}'.format(round( w**2*R/(g*np.sin(a)), 2)) ).replace('.', '{,}') )
    plt.figtext(0.67, 0.73, r'$mg\sin\alpha = {}\;\textrm{{Н}}$'.format(round(m*g*np.sin(a)) ) )

    ax.set_xlabel(r'$t, \textrm{с}$')
    ax.set_ylabel(r'$F_\textrm{тр},\;\textrm{Н}$', labelpad=13)
    ax.grid()
    ax.legend(loc='upper center', bbox_to_anchor=(0.5, 1.6), ncol=1, fancybox=False, shadow=False)
    ax.set_ylim([0,42])

    plt.savefig('/Users/slisakov/Yandex.disk.localized/documents/scripts/1514_school/237/' + str('{:0.3f}'.format(round(R,3)))+'.pdf', bbox_inches='tight')
    plt.close()
    
    # Then do
    # convert -loop 0 *pdf 237.gif
    # using imagemagick