Plot for https://phys.pro/problems/1079

1079.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

# Plot setup {{{
lw = 2
rcParams['font.size'] = 23
#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}')

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",
})

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.xaxis.set_major_formatter(FuncFormatter(format_decimal))

# def custom_formatter(x, pos):
#     return "{:.2f}".format(x).replace('.', ',')
# ax.yaxis.set_major_formatter(FuncFormatter(custom_formatter))
#}}}

m = 0.1
g = 10
L = 1.5/2
l = 1.2/2
x = np.linspace(1e-20, L*0.99999, 100000)

sin_alpha = (L-x) / L
cos_alpha = np.sqrt(L**2 - (L-x)**2) / L
tg_alpha = sin_alpha / cos_alpha

v = np.sqrt(2*g) * (2*L*x-x**2)**(3/4) / (L**2+2*L*x-x**2)**(1/2)
v3 = v * tg_alpha

a = np.sqrt(2*g) * v * (L-x)*(-x**2/2 + L*x + 3*L**2/2) / ((L**2 + 2*L*x - x**2)**(3/2) * (x*(2*L-x))**(1/4))
a3_der = np.sqrt(2*g) * v * (L**4/2 - 4*L**3*x + 2*L*x**3 - x**4/2) / ((L**2 + 2*L*x - x**2)** (3/2) * (2*L*x-x**2)**(3/4) )

T = m*a / sin_alpha
a3_dyn = (m*g - 2*T*cos_alpha) / m

lw = 2.3

## PLOT a(x)
ax.plot(x,a, label='$a$ (крайние бусинки)', lw=lw)
ax.plot(x,a3_der, label='$a_3$ (нижняя бусинка)', lw=lw, color='C3')
ax.plot(x,a*tg_alpha, label='$a_3$ (авторское)', lw=lw*0.8, ls=(0,(4,2.8)), color='C2')
ax.set_ylabel(r'$a, \text{м}/\text{с}^2$', labelpad=13)

### PLOT v(x)
#ax.plot(x,v, label='$ʋ$ (крайние бусинки)', lw=lw, color='C0')
#ax.plot(x,v3, label='$ʋ_3$ (нижняя бусинка)', lw=lw, color='C3')
#ax.set_ylabel(r'$ʋ, \text{м}/\text{с}$', labelpad=13)

### PLOT T(x)
#ax.plot(x,T, label='$T$', lw=lw, color='C0')
#ax.set_ylabel(r'$T,$ Н', labelpad=13)
#ax.yaxis.set_major_formatter(FuncFormatter(format_decimal))


plt.figtext(0.23, 0.73, r'$m = {}$ кг'.format(m).replace('.', '{,}') )

ax.set_xlabel(r'$x,$м')

#ax.plot(x,T, label='$T$', lw=lw)
#ax.plot(x,Ts, label='$T\'$', lw=lw)
#ax.plot([0,L], [m*g, m*g], label='$mg$', lw=lw)

ax.set_xticks([0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.75])

ax.legend()
ax.grid()

plt.show()

#a3 = - sqrt(g) * sqrt(-x**2+2*L*x+L**2) * (x**4-4*l*x**3+8*l**3*x-l**4) * xdot / (2*L*x-x**2)**(3/4) * sqrt(2) * (x**4 - 4*L*x**3 + 2*L**2*x**2 + 4*L**3*x + L**4)
#a3 = sqrt(2*g) * xdot * (L**4/2 - 4*L**3*x + 2*L*x**3 - x**4/2) / (L**2 + 2*L*x - x**2)**(3/2) * (2*L*x-x**2)**(3/4)
#a = np.sqrt(g) * np.sqrt(-x**2 + 2*L*x + L**2) * (np.sqrt(2)*x**3 - 3*np.sqrt(2)*L*x**2 - np.sqrt(2)*L**2*x + 3*np.sqrt(2)*L**3) * xdot / ((2*l*x - x**2)**(1/4) * (2*x**4 - 8*l*x**3 + 4*l**2*x**2 + 8*l**3*x + 2*l**4))
#a = sqrt(2*g) * xdot * (L-x) * (-x**2/2+L*x+3*L**2/2) / ((L**2 + 2*L*x - x**2)**(3/2) * (2*L*x-x**2)**(1/4))