首先我們將theta作為橫坐標，omega作為縱坐標，同時變化F_D的參數(shù)，比較這兩種情況下擺的混沌效應(yīng)．
-q\frac{d\theta}{dt}+F_Dsin(\Omega_D t))

• sin\theta_i-q\omega_i+F_Dsin(\Omega_Dt_i)]\Delta t)
• 
• if \theta_{i+1} is out of the range[-pi,pi],add or substract 2pi to keep it in the range.
• 
• Repeat

代碼實現(xiàn)

def swing(self):
        loop = True
        i = 0
        while(loop):
            self.omega.append(self.omega[i] + (-self.g_l * math.sin(self.theta[i]) - self.q * self.omega[i] +
                                                   self.f_d * math.sin(self.omega_d * self.t[i])) * self.dt)
            self.temp = self.theta[i] + self.omega[i + 1] * self.dt
            if math.pi < self.temp:
                self.temp -= 2 * math.pi
            elif - math.pi > self.temp:
                self.temp += 2 * math.pi
            self.theta.append(self.temp)
            self.t.append(self.t[i] + self.dt)
            i += 1
            if self.total_time < self.t[i]:
                loop = False

Then we only plot omega versus theta only at times that are in phase with the driving force.
That is,we only display the point when
where n is an integer.

• 也就是說，當滿足
  時，我們就將相應(yīng)的點放置上去

代碼實現(xiàn)

def Omega2Theta(self):
        self.swing()
        loop = True
        i = 0
        n = 0
        while(loop):
            # omega_D * t = 2 * pi * n
            if (self.t[i] > (2*n+1)*math.pi/self.omega_d):
                n += 1
            if (abs(self.t[i] - 2 * n * math.pi/self.omega_d) < (self.dt/2)):
                self.theta_ps.append(self.theta[i])
                self.omega_ps.append(self.omega[i])
            i += 1
            if self.total_time < self.t[i]:
                loop = False

接下來讓我們變化一下參數(shù)：

我們觀察一下\theta與ｔ在變化的驅(qū)動力下的關(guān)系圖

• 致謝
  　盧江瑋的代碼助攻～