def anim_orb(x):
fig, ax = plt.subplots()
R_max = np.max(R) + 1
line = [ax.plot([], [])[0] for _ in range(n)]
line.extend([ax.plot([], [], "ok")[0] for _ in range(n)])
line.append(ax.plot([], [], "oy")[0])
ax.set_ylim((-R_max, R_max))
ax.set_xlim((-R_max, R_max))
frameskip = 12
tail_length = int(1 / dt)
def animate(frame):
frame = frame * frameskip + tail_length
total = []
for i in range(n):
xi = x[frame - tail_length:frame, i, 0]
line[i].set_data(xi[:, 0], xi[:, 1])
line[n + i].set_data(xi[-1, 0], xi[-1, 1])
line[-1].set_data(0, 0)
return line
a = anim(fig, animate, interval=1)
plt.show()
# (x, y, z)' = f(x, y, z)
def f(x, y, z):
s = 10
r = 28
b = 8 / 5.
return np.array([-s * x + s * y, -x * z + r * x - y, x * y - b * z],
dtype=np.float)
def setAx(ax):
ax.cla()
ax.set_zlim(10, 40)
ax.axis((-20, 20, -20, 20))
ax.set_axis_off()
def y(n):
global ys, ye, ax
setAx(ax)
ys = np.concatenate([ys, [RKStep(f, ys[-1], A, b, 0.01)]])
ye = np.concatenate([ye, [RKStep(f, ye[-1], Ae, be, 0.01)]])
return ax.plot(*ys.T) + ax.plot(*ye.T)
if __name__ == "__main__":
ys = np.array([np.array([10, 0.1, 25.])])
ye = np.copy(ys)
fig = plt.figure()
ax = Axes3D(fig)
a = anim(fig, y, interval=10, blit=True)
plt.show()
def runn():
p = Kepler(v0=8.5)
p.solve(N=200)
# Gráficos
plt.style.use('dark_background')
fig = plt.figure(figsize=(14, 8))
gs = fig.add_gridspec(1, 2)
ax1 = fig.add_subplot(gs[0, 0], polar=True)
ax1.plot(p.th, p.r, 'g--', 'origem')
plt.scatter(820, 2.3, s=350, color='yellow')
ptraj, = ax1.plot([p.th[0]], [p.r[0]], 'ro')
## ax2 eh mais importante
ax2 = fig.add_subplot(gs[0, 1], polar=False)
r, V, Vcf, Vef = p.Energia_graficos(rmin=.2, rmax=p.r.max() + 8)
ax2.axvline(0, color='purple')
ax2.axhline(0, color='purple')
ax2.set_xlabel('$r$ (ua)')
ax2.set_ylabel('Energias')
ax2.set_ylim(-40, 40)
ax2.plot(r, V, 'g--', label=f'$V(r)$')
ax2.plot(r, Vcf, 'y--', label=f'$V_{{cf}}(r)$')
ax2.plot(r, Vef, 'b', label=f'$V_{{ef}}(r)$')
T, = ax2.plot([], [], 'k-', label=f'$T_{{ef}}(\\dot r)$')
ax2.plot(p.r, p.E, label=f'$E$')
E, = ax2.plot(p.r[0], p.E[0], 'ro', markersize=3)
V, = ax2.plot(p.r[0], p.V[0], 'ro', markersize=3)
Vef, = ax2.plot(p.r[0], p.Vef[0], 'ro', markersize=3)
Vcf, = ax2.plot(p.r[0], p.Vcf[0], 'ro', markersize=3)
tempo = ax2.text(.65, .02, 't = 0', transform=ax2.transAxes)
plt.legend(loc='upper right')
def updatefig(i):
global n, pause
if not pause:
ptraj.set_data([p.th[n]], [p.r[n]])
T.set_data([p.r[n], p.r[n]], [p.E[n], p.Vef[n]])
V.set_data(p.r[n], p.V[n])
Vcf.set_data(p.r[n], p.Vcf[n])
Vef.set_data(p.r[n], p.Vef[n])
E.set_data(p.r[n], p.E[n])
tempo.set_text(f't={p.t[n]:.2f} anos')
#rt.set_data([p.t[n]], [p.r[n]])
#tht.set_data([p.t[n]], [p.th[n]])
#rp.set_data([p.t[n]], [p.rp[n]])
#thp.set_data([p.t[n]], [p.thp[n]])
n = n + 1 if n < p.t.size - 1 else 0
return ptraj, tempo, Vef, Vcf, V, E, T
def onClick(event):
global pause
pause ^= True
fig.canvas.mpl_connect('button_press_event', onClick)
n = 0
a = anim(fig, updatefig, frames=p.t.size, interval=2, blit=True)
fig.tight_layout()
plt.show()
global l1, l2
x1 = l1 * sin(b[0][0])
y1 = -l1 * cos(b[0][0])
x2 = x1 + l2 * sin(b[1][0])
y2 = y1 - l2 * cos(b[1][0])
return ([0, x1, x2], [0, y1, y2])
fig = plt.figure()
ax = fig.add_subplot(111, xlim=(-2.5, 2.5), ylim=(-2.5, 2.5))
lines = [ax.plot([], [], "o-") for i in range(N)]
def animate(n):
global bs
# Several timesteps increas prec. w/o need for high framerate / slow motion
for i in range(100):
bs = updateState(bs)
for i in range(N):
lines[i][0].set_data(*getXY(bs[i]))
return lines
a = anim(fig, animate, frames=2000)
if os.path.isfile("dp_frames"):
shutil.rmtree("dp_frames")
a.save("dp.html", fps=24)
def run_mhs():
class dp_mola:
def __init__(self, mu=.5, k=2):
self.mu = mu
self.k = k
self.w2 = k / mu
self.tau = 2 * np.pi / np.sqrt(self.w2)
def EDO(self, Y, t):
x, y, xp, yp = Y
dx = xp
dy = yp
dxp = -self.w2 * x
dyp = -self.w2 * y
return dx, dy, dxp, dyp
def set_CI(self, x0=1., y0=0, v0x=0, v0y=1):
self.Y0 = [x0, y0, v0x, v0y]
self.L = self.mu * (x0 * v0y - y0 * v0x)
def solve(self, tmax=None, N=1000):
if tmax is None:
tmax = self.tau
self.t = np.linspace(0, tmax, N)
self.Y = spi.odeint(self.EDO, self.Y0, self.t)
self.x, self.y, self.vx, self.vy = self.Y.T
self.r2 = self.x**2 + self.y**2
self.v2 = self.vx**2 + self.vy**2
self.r = np.sqrt(self.r2)
self.v = np.sqrt(self.v2)
self.th = np.fmod(np.arctan2(self.y, self.x), 2 * np.pi)
self.th[self.th < 0] = self.th[self.th < 0] + 2 * np.pi
self.thp = self.L / self.mu / self.r2
self.rp = np.sqrt(self.v2 - (self.r * self.thp)**2)
self.Energia()
def Energia(self):
self.T = .5 * self.mu * self.v2
self.V = .5 * self.k * self.r2
self.E = self.T + self.V
self.Vcf = .5 * self.L**2 / self.mu / self.r2
self.Veq = self.V + self.Vcf
def Energia_graficos(self, N=200, rmin=.3, rmax=1.6):
r = np.linspace(rmin, rmax, N)
V = .5 * self.k * r**2
Vcf = .5 * (self.L / r)**2 / self.mu
Veq = V + Vcf
return r, V, Vcf, Veq
s = dp_mola()
s.set_CI()
s.solve()
# gráficos
style.use('dark_background')
fig = plt.figure(figsize=(10, 6))
gs = fig.add_gridspec(2, 1)
ax2 = fig.add_subplot(gs[0, 0])
ax2.set_xlabel('$r$')
ax2.set_ylabel('Energias')
r, V, Vcf, Veq = s.Energia_graficos()
ax2.plot(r, V, '--', label='V')
ax2.plot(r, Vcf, '--', label='Vcf')
ax2.plot(r, Veq, 'b', label='Veq')
Teq, = ax2.plot([s.r[0], s.r[0]], [s.Veq[0], s.E[0]],
'b-',
marker='o',
markerfacecolor='red',
label='Teq')
ax2.plot(s.r, s.E, label='E')
V, = ax2.plot(s.r[0], s.V[0], 'ro')
Vcf, = ax2.plot(s.r[0], s.Vcf[0], 'ro')
plt.legend()
ax3 = fig.add_subplot(gs[1, 0])
ax3.set_xlabel('$t$')
ax3.set_ylabel('$r$')
ax3.plot(s.t, s.r, 'b--')
rplot, = ax3.plot(s.t[0], s.r[0], 'ro')
def updatefig(i):
global n
if not pause:
Teq.set_data([s.r[n], s.r[n]], [s.Veq[n], s.E[n]])
V.set_data(s.r[n], s.V[n])
Vcf.set_data(s.r[n], s.Vcf[n])
rplot.set_data(s.t[n], s.r[n])
n = n + 1 if n < s.t.size - 1 else 0
return Teq, Vcf, V, rplot
def onClick(event):
global pause
pause ^= True
fig.canvas.mpl_connect('button_press_event', onClick)
a = anim(fig, updatefig, frames=s.t.size, interval=1, blit=True)
fig.tight_layout()
plt.show()