diff options
Diffstat (limited to '')
| -rw-r--r-- | buch/papers/kra/scripts/animation.py | 243 | ||||
| -rw-r--r-- | buch/papers/kra/scripts/simulation.py | 40 |
2 files changed, 283 insertions, 0 deletions
diff --git a/buch/papers/kra/scripts/animation.py b/buch/papers/kra/scripts/animation.py new file mode 100644 index 0000000..5e805ae --- /dev/null +++ b/buch/papers/kra/scripts/animation.py @@ -0,0 +1,243 @@ +import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib.patches
+import matplotlib.transforms
+import matplotlib.text
+from matplotlib.animation import FuncAnimation
+import imageio
+
+from simulation import Simulation
+
+
+class Mass:
+ def __init__(self, x_0, width, height, **kwargs):
+ self._x_0 = x_0
+ xy = (x_0, 0)
+ self._rect = matplotlib.patches.Rectangle(xy, width, height, **kwargs)
+
+ @property
+ def patch(self):
+ return self._rect
+
+ @property
+ def x(self):
+ return self._rect.get_x()
+
+ @property
+ def width(self):
+ return self._rect.get_width()
+
+ def move(self, x):
+ self._rect.set_x(self._x_0 + x)
+
+
+class Spring:
+ def __init__(self, n, height, ax, resolution=1000, **kwargs):
+ self._n = n
+ self._height = height
+ self._N = resolution
+ (self._line,) = ax.plot([], [], "-", **kwargs)
+
+ def set(self, x_0, x_1):
+ T = (x_1 - x_0) / self._n
+ x = np.linspace(x_0, x_1, self._N, endpoint=True)
+ t = np.linspace(0, x_1 - x_0, self._N)
+ y = (np.sin(2 * np.pi * t / T) + 1.5) * self._height / 2
+ self.line.set_data(x, y)
+
+ @property
+ def line(self):
+ return self._line
+
+
+class LinePlot:
+ def __init__(self, ax, **kwargs):
+ (self._line,) = ax.plot([], [], "-", **kwargs)
+ self._x = []
+ self._y = []
+
+ @property
+ def line(self):
+ return self._line
+
+ def update(self, x, y):
+ self._x.append(x)
+ self._y.append(y)
+ self._line.set_data(self._x, self._y)
+
+
+class ScatterPlot:
+ def __init__(self, ax, **kwargs):
+ self._color = kwargs.get("color", "tab:green")
+ self._line = ax.scatter([], [], **kwargs)
+ self._ax = ax
+ self._x = []
+ self._y = []
+
+ @property
+ def line(self):
+ return self._line
+
+ def update(self, x, y, **kwargs):
+ self._x.append(x)
+ self._y.append(y)
+ self._line.remove()
+ self._line = self._ax.scatter(self._x, self._y, color=self._color, **kwargs)
+
+
+class QuiverPlot:
+ def __init__(self, ax, **kwargs):
+ self.x = []
+ self.y = []
+ self.u = []
+ self.v = []
+ self.ax = ax
+ self.ln = self.ax.quiver([], [], [], [])
+
+ def update(self, x, y, u, v):
+ self.x.append(x)
+ self.y.append(y)
+ self.u.append(u)
+ self.v.append(v)
+ self.ln.remove()
+ self.ln = self.ax.quiver(self.x, self.y, self.u, self.v)
+
+ @property
+ def line(self):
+ return self.ln
+
+
+anim_folder = "anim_0"
+img_counter = 0
+
+sim = Simulation()
+params = {
+ "x_0": [2, -2],
+ "k_1": 1,
+ "k_c": 2,
+ "k_2": 1,
+ "m_1": 0.5,
+ "m_2": 0.5,
+}
+
+time = 2.1
+
+
+# create axis
+fig = plt.figure(figsize=(20, 15), constrained_layout=True)
+fig.suptitle(
+ " ,".join([f"${key} = {val}$" for (key, val) in params.items()]), fontsize=20
+)
+spec = fig.add_gridspec(3, 4)
+ax0 = fig.add_subplot(spec[-1, :])
+ax1 = fig.add_subplot(spec[:-1, :2])
+ax2 = fig.add_subplot(spec[:-1, 2:])
+
+ax0.set_yticks([])
+
+mass_height = 0.5
+spring_height = 0.6 * mass_height
+x_max = 21
+y_max = 2 * mass_height
+
+mass_1 = Mass(
+ 7,
+ 2,
+ mass_height,
+ color="tab:red",
+)
+mass_2 = Mass(14, 2, mass_height, color="tab:blue")
+masses = [mass_1, mass_2]
+patches = [mass.patch for mass in masses]
+
+spring_1 = Spring(4, spring_height, ax0, color="tab:red", linewidth=10)
+spring_2 = Spring(4, spring_height, ax0, color="tab:gray", linewidth=10)
+spring_3 = Spring(4, spring_height, ax0, color="tab:blue", linewidth=10)
+springs = [spring_1, spring_2, spring_3]
+
+linePlot_1 = LinePlot(ax1, color="tab:red", label="$m_1$", alpha=1)
+linePlot_2 = LinePlot(ax1, color="tab:blue", label="$m_2$", alpha=1)
+linePlots = [linePlot_1, linePlot_2]
+
+# quiverPlot = QuiverPlot(ax2)
+scatterPlot = ScatterPlot(ax2)
+
+lines = [spring.line for spring in springs]
+lines.extend([plot.line for plot in linePlots])
+# lines.append(quiverPlot.line)
+lines.append(scatterPlot.line)
+
+objects = lines + patches
+
+ax0.plot(
+ np.repeat(mass_1.x, 2),
+ [0, y_max],
+ "--",
+ color="tab:red",
+ label="Ruhezustand $m_1$",
+)
+ax0.plot(
+ np.repeat(mass_2.x, 2),
+ [0, y_max],
+ "--",
+ color="tab:blue",
+ label="Ruhezustand $m_2$",
+)
+
+
+def init():
+ ax0.set_xlim(0, x_max)
+ ax0.set_ylim(0, y_max)
+
+ ax1.set_xlim(0, time)
+ ax1.set_ylim(-4, 4)
+ ax1.set_xlabel("time", fontsize=20)
+ ax1.set_ylabel("$q$", fontsize=20)
+
+ ax2.set_xlim(-4, 4)
+ ax2.set_ylim(-4, 4)
+ ax2.set_xlabel("$q_1$", fontsize=20)
+ ax2.set_ylabel("$q_2$", fontsize=20)
+
+ for patch in patches:
+ ax0.add_patch(patch)
+
+ spring_1.set(0, mass_1.x)
+ spring_2.set(mass_1.x + mass_1.width, mass_2.x)
+ spring_2.set(mass_2.x + mass_2.width, x_max)
+
+ return objects
+
+
+def update(frame):
+ global img_counter
+ x_1, x_2 = sim(frame, **params)
+
+ mass_1.move(x_1)
+ mass_2.move(x_2)
+
+ spring_1.set(0, mass_1.x)
+ spring_2.set(mass_1.x + mass_1.width, mass_2.x)
+ spring_3.set(mass_2.x + mass_2.width, x_max)
+
+ linePlot_1.update(frame, x_1)
+ linePlot_2.update(frame, x_2)
+
+ scatterPlot.update(x_1, x_2, alpha=0.25)
+
+ img_counter += 1
+ return objects
+
+
+anim = FuncAnimation(
+ fig,
+ update,
+ frames=np.linspace(0, time, int(time * 30)),
+ init_func=init,
+ blit=False,
+)
+
+ax0.legend(fontsize=20)
+ax1.legend(fontsize=20)
+FFwriter = matplotlib.animation.FFMpegWriter(fps=30)
+anim.save("animation.mp4", writer=FFwriter)
diff --git a/buch/papers/kra/scripts/simulation.py b/buch/papers/kra/scripts/simulation.py new file mode 100644 index 0000000..8bccb6a --- /dev/null +++ b/buch/papers/kra/scripts/simulation.py @@ -0,0 +1,40 @@ +import sympy as sp
+
+
+class Simulation:
+ def __init__(self):
+ self.k_1, self.k_2, self.k_c = sp.symbols("k_1 k_2 k_c")
+ self.m_1, self.m_2 = sp.symbols("m_1 m_2")
+ self.t = sp.symbols("t")
+ K = sp.Matrix(
+ [[-(self.k_1 + self.k_c), self.k_c], [self.k_c, -(self.k_2 + self.k_c)]]
+ )
+ M = sp.Matrix([[1 / self.m_1, 0], [0, 1 / self.m_2]])
+ A = M * K
+
+ self.eigenvecs = []
+ self.eigenvals = []
+ for ev, mult, vecs in A.eigenvects():
+ self.eigenvecs.append(sp.Matrix(vecs))
+ self.eigenvals.extend([ev] * mult)
+
+ def __call__(self, t, x_0, k_1, k_c, k_2, m_1, m_2):
+ params = {
+ self.k_1: k_1,
+ self.k_c: k_c,
+ self.k_2: k_2,
+ self.m_1: m_1,
+ self.m_2: m_2,
+ }
+ x_0 = sp.Matrix(x_0)
+ eig_mat = sp.Matrix.hstack(*self.eigenvecs).subs(params)
+ g = eig_mat.inv() * x_0
+ L = sp.Matrix(
+ [
+ g[0] * sp.cos(self.eigenvals[0].subs(params) * self.t),
+ g[1] * sp.cos(self.eigenvals[1].subs(params) * self.t),
+ ]
+ )
+ x = eig_mat * L
+ f = sp.lambdify(self.t, x, "numpy")
+ return f(t).squeeze()
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