Code
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as mpl
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as mpl
'figure.figsize']=(4,4) plt.rcParams[
Sei \(f:\mathbb{R} \rightarrow \mathbb{R}^2\) die Kurve \(f(t)= \begin{pmatrix} x(t) \\ y(t) \end{pmatrix} = \sqrt{t}\begin{pmatrix} \cos(\pi t) \\ \sin(\pi t) \end{pmatrix}\)
quiver
Geschwindigkeitsvektoren in Ihren Plot ein. Tipp: Verwenden Sie die scale
-Option.Gegeben ist die Kurve \(\begin{pmatrix} x(t) \\ y(t) \end{pmatrix} = \begin{pmatrix} \sin(2t) \\ \cos(3t) \end{pmatrix}\).
Gegeben ist das Skalarfeld \(\phi(x,y,z)=10 x^2 y^3 - 5 xyz^2\).
Gegeben ist das Vektorfeld \(\mathbf{F}=\begin{pmatrix} xy^2 \\ x^2y-4y \end{pmatrix}\).
= np.linspace(0.01, 2)
t
= np.sqrt(t)*np.cos(np.pi*t)
x = np.sqrt(t)*np.sin(np.pi*t)
y
= 0.5/np.sqrt(t)*np.cos(np.pi*t) - np.pi*np.sqrt(t)*np.sin(np.pi*t)
xp = 0.5/np.sqrt(t)*np.sin(np.pi*t) + np.pi*np.sqrt(t)*np.cos(np.pi*t)
yp
plt.figure()'r')
plt.plot(x, y, ='xy', scale= 3)
plt.quiver(x, y, xp, yp, scale_units'x')
plt.xlabel('y')
plt.ylabel(-2, 2)
plt.xlim(-2, 2)
plt.ylim(True) plt.grid(
= np.sqrt(t)
r = np.pi*t
phi
= 0.5/np.sqrt(t)
rp = np.pi*np.ones(r.shape) phip
plt.figure()'r')
plt.plot(r, phi, ='xy', scale= 4)
plt.quiver(r, phi, rp, phip, scale_units'r')
plt.xlabel('phi')
plt.ylabel(0, 8)
plt.xlim(0, 8)
plt.ylim(True) plt.grid(
= np.linspace(-3, 3, 500)
t = np.sin(2*t)
x = np.cos(3*t)
y
plt.figure()'--r')
plt.plot(x, y,'x')
plt.xlabel('y')
plt.ylabel(True) plt.grid(
\(\nabla \phi=\begin{pmatrix} \partial \phi / \partial x \\ \partial \phi / \partial y \\ \partial \phi / \partial z \end{pmatrix} = \begin{pmatrix} 20 x y^3-5 y z^2 \\ 30 x^2 y^2-5 x z^2 \\ -10 x y z \end{pmatrix}\)
\(\left.\nabla \phi \right|_P=\begin{pmatrix} 0 \\ 10 \\ 20 \end{pmatrix} \rightarrow \left|\left.\nabla \phi \right|_P \right|=\sqrt{10^2+20^2}=\sqrt{500}=22.36\)
= np.arange(-5, 5, 1)
x = np.arange(-5, 5, 1)
y = np.meshgrid(x,y)
X, Y = [X*Y**2,X**2*Y-4*Y]
U,V
= plt.subplots()
fig, ax = ax.quiver(X, Y, U, V)
q =mpl.Circle((0,0),2,facecolor='none',ec='darkred')
circle
ax.add_patch(circle)'equal', adjustable='box') ax.set_aspect(