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LiveInternet.ru:
: 17.03.2011
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: 51

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[ ] Python ?

, 07 2017 . 14:02 +
! - ( ) : ? , ,

image

? - ? .

:

$$display$$\dfrac{m \dot{\theta }^2}{2}+mgl(1-cos \ \theta )=E$$display$$


$$display$$\ddot{\theta}+gl \ sin \ \theta=0$$display$$


$$display$$sin \ x\approx x$$display$$

, , g. , , , scipy .


$$display$$\dfrac{d}{dt}\begin{pmatrix} \theta \\ \omega \end{pmatrix}=\begin{pmatrix} \omega \\ -gl \ sin\ \theta \end{pmatrix} $$display$$


( scipy.integrate.odeint, , ).

t = linspace(0,15,100)
G = 9.8
L = 1.0

def diffeq(state, t):
    th, w = state
    return [w, -G*L*sin(th)]
dt = 0.05
t = np.arange(0.0, 20, dt)

th1 = 179.0
w1 = 0.0
state = np.radians([th1, w1])
y = odeint(diffeq, state, t)

, . - , : , ?

N ( ) !

?

$$display$$a = a_{central} - g \ cos \ \theta, a_{central} = \dot{\theta}^2 r \\ \ddot{\theta} = gx \ sin \ \theta$$display$$


? , , .

r . scipy:

$$display$$\begin{cases} \ddot{r} = \dot{\theta}^2r-g \ cos \ \theta, \\ \ddot{\theta} = gr \ sin \ \theta \end{cases}$$display$$


image
image
import matplotlib.animation as animation
from pylab import *
from scipy.integrate import *
import matplotlib.pyplot as plt

t = linspace(0,15,100)
G = 9.8
L = 10.0

def derivs(state, t):
    th, w, r, v  = state
    if 0. 0, max = L))*sin(y[:, 0])
y2 = -(L-y[:,2].clip(min = 0, max = L))*cos(y[:, 0])

fig = plt.figure()
ax = fig.add_subplot(111, autoscale_on=False, xlim=(-L-0.2, L+0.2), ylim=(-L-0.2, L+0.2))
ax.grid()

line, = ax.plot([], [], '-', lw=2)
point, = ax.plot(0,0,'o', lw=2)
extra, = ax.plot(x1/L*r1,y1/L*r1,'o', lw=2)
time_template = 'time = %.1fs'
time_text = ax.text(0.05, 0.9, '', transform=ax.transAxes)


def init():
    line.set_data([], [])
    point.set_data(0,0)
    time_text.set_text('')
    extra.set_data(x1/L*r1,y1/L*r1)
    return line, time_text, point, extra

def animate(i):
    thisx = [0, x1[i]]
    thisy = [0, y1[i]]
    thisx2 = x2[i]
    thisy2 = y2[i]
    point.set_data(thisx[0],thisy[0])
    line.set_data(thisx, thisy)
    time_text.set_text(time_template % (i*dt))
    extra.set_data([thisx2,thisy2])
    
    return line, time_text, point, extra

ani = animation.FuncAnimation(fig, animate, np.arange(1, len(y)),
                              interval=25, blit=True, init_func=init, repeat = False)

plt.show()

P.S. .
P.S.S. ( ) .

, , !
Original source: habrahabr.ru (comments, light).

https://habrahabr.ru/post/332620/

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