116 lines
3.1 KiB
Python
116 lines
3.1 KiB
Python
"""
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https://en.wikipedia.org/wiki/Ellipse#General_parametric_form
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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class Pendel():
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def __init__(self, a: float, b: float, omega: float, phi: float, delta: float, tau: float, sub: int = 0):
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self.a = a
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self.b = b
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self.omega = omega
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self.phi = phi
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self.delta = delta
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self.tau = tau
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self._sub = sub
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def point(self, t: float):
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x = (self.a * np.cos(t*self.omega + self.delta)*np.cos(t*self.phi)
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- self.b*np.sin(t*self.omega + self.delta)*np.sin(t*self.phi))
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y = (self.a * np.cos(t*self.omega + self.delta)*np.sin(t*self.phi)
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+ self.b*np.sin(t*self.omega + self.delta)*np.cos(t*self.phi))
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return np.exp(-t*self.tau)*np.array([x, y])
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def __repr__(self):
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SUB = str.maketrans("0123456789", "₀₁₂₃₄₅₆₇₈₉")
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sub = f"{self._sub}".translate(SUB)
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return f"A{sub}={self.a}, B{sub}={self.b}, ω{sub}={self.omega}, Φ{sub}={self.phi}, δ{sub}={self.delta}, τ{sub}={self.tau}"
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def update(self, **kwargs):
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for key, val in kwargs.items():
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if hasattr(self, key):
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setattr(self, key, val)
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else:
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raise ValueError(f'{self.__name__} object has no attribute {key}')
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class DoppelPendel():
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def __init__(self, kwargs1, kwargs2):
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self.stift = Pendel(**kwargs1, sub=1)
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self.tisch = Pendel(**kwargs2, sub=2)
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def point(self, t):
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return self.stift.point(t)+self.tisch.point(t)
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def update_stift(self, **kwargs):
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self.stift.update(**kwargs)
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def update_tisch(self, **kwargs):
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self.tisch.update(**kwargs)
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def __repr__(self):
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return str(self.stift) + "\n" + str(self.tisch)
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class Harmonograph(DoppelPendel):
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def __init__(self, kwargs1, kwargs2, t_init, n=10000):
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super().__init__(kwargs1, kwargs2)
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self.n = n
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self.t = t_init
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self.fig, self.ax = plt.subplots()
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self.ax.set_xlim(-2, 2)
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self.ax.set_ylim(-2, 2)
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self.ax.set_aspect('equal')
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self.ax.axis('off')
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self.init_harmonograph()
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# self.label = self.ax.text(0, -2, str(self),
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# horizontalalignment='center',
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# verticalalignment='bottom',)
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def init_harmonograph(self):
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t = np.linspace(0, self.t, self.n)
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self.ax.plot(*self.point(t), 'k', lw=0.5)
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if __name__ == "__main__":
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# kw1 = dict(
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# a=1,
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# b=1,
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# omega=np.pi/60,
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# phi=np.pi/180,
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# delta=np.pi/2,
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# tau=0
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# )
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# kw2 = dict(
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# a=0.2,
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# b=1,
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# omega=0.1204277183860873,
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# phi=np.pi/90,
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# delta=0,
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# tau=0
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# )
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kw1 = dict(
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a=1,
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b=0.3,
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omega=0.05,
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phi=2.5e-4,
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delta=0,
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tau=5e-7
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)
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kw2 = dict(
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a=0.5,
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b=0,
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omega=1/10,
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phi=5e-5,
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delta=0,
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tau=5e-5
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)
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p1 = Harmonograph(kw1, kw2, 7000)
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plt.show()
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