Double pendulum animation in python - numerical-methods

Question

I am using the following code to solve the system of differential equations numerically and then animate it:
for i in range(steps-1):
Theta1 = t1[i]
Theta2 = t2[i]
dTheta1 = w1[i]
dTheta2 = w2[i]
a1 = (g*(np.sin(Theta2)*np.cos(Theta1-Theta2)-mu*np.sin(Theta1))-(l2*dTheta2*dTheta2+l1*dTheta1*dTheta1*np.cos(Theta1-Theta2))*np.sin(Theta1-Theta2))/(l1*(mu-np.cos(Theta1-Theta2)*np.cos(Theta1-Theta2)))
a2 = (mu*g*(np.sin(Theta1)*np.cos(Theta1-Theta2)-np.sin(Theta2))+(mu*l1*dTheta1*dTheta1+l2*dTheta2*dTheta2*np.cos(Theta1-Theta2))*np.sin(Theta1-Theta2))/(l2*(mu-np.cos(Theta1-Theta2)*np.cos(Theta1-Theta2)))
w1[i+1] = w1[i] + dt*a1
w2[i+1] = w2[i] + dt*a2
t1[i+1] = t1[i] + dt*w1[i]
t2[i+1] = t2[i] + dt*w2[i]
This gives me errors such as
RuntimeWarning: invalid value encountered in longdouble_scalars
and
RuntimeWarning: overflow encountered in longdouble_scalars.
At first, I thought this might be happening due to precisions errors, so I tried using longdouble. But that didn't help at all. When I run the animation, I get a few frames of unphysical systems and then it shuts downs. I have checked my equation from multiple sources and I ended up using their equations too and the problem still persists. What am I doing wrong?
Edit: Okay so simply decreasing the step size seemed to not give me the error any more, but now animation is unphysical. The pendulum seems to pick up speed over time, and also performs full rotations, even when it started from rest at an extreme. I am using a 4th order RK method and still getting this problem. Any ideas? I have provided my new code below
def diff_eq_a1(theta1,theta2,w1,w2):
a11 = mu
a12 = np.cos(theta1-theta2)
a21 = np.cos(theta1-theta2)
a22 = 1
b1 = (mu*g*l1*np.sin(theta1)) + (l2*np.sin(theta1-theta2)*w2*w2)
b2 = (g*l2*np.sin(theta2))-(l1*np.sin(theta1-theta2)*w1*w1)
return -(1/l1)*(b1*a22-b2*a12)/(a11*a22-a21*a12)
def diff_eq_a2(theta1,theta2,w1,w2):
a11 = mu
a12 = np.cos(theta1-theta2)
a21 = np.cos(theta1-theta2)
a22 = 1
b1 = (mu*g*l1*np.sin(theta1)) + (l2*np.sin(theta1-theta2)*w2*w2)
b2 = (g*l2*np.sin(theta2))-(l1*np.sin(theta1-theta2)*w1*w1)
return -(1/l2)*(b2*a11-b1*a21)/(a11*a22-a21*a12)
for i in range(steps-1):
a1_k1 = dt*diff_eq_a1(t1[i],t2[i],w1[i],w2[i])
a1_k2 = dt*diff_eq_a1((t1[i]+0.5*a1_k1),t2[i],w1[i],w2[i])
a1_k3 = dt*diff_eq_a1((t1[i]+0.5*a1_k2),t2[i],w1[i],w2[i])
a1_k4 = dt*diff_eq_a1((t1[i]+a1_k3),t2[i],w1[i],w2[i])
w1[i+1] = w1[i] + (a1_k1/6)+(a1_k2/3)+(a1_k3/3)+(a1_k4/6)
a2_k1 = dt*diff_eq_a1(t1[i],t2[i],w1[i],w2[i])
a2_k2 = dt*diff_eq_a1(t1[i],(t2[i]+0.5*a2_k1),w1[i],w2[i])
a2_k3 = dt*diff_eq_a1(t1[i],(t2[i]+0.5*a2_k2),w1[i],w2[i])
a2_k4 = dt*diff_eq_a1(t1[i],(t2[i]+a2_k3),w1[i],w2[i])
w2[i+1] = w2[i] + (a2_k1/6)+(a2_k2/3)+(a2_k3/3)+(a2_k4/6)
t1[i+1] = t1[i] + dt*w1[i]
t2[i+1] = t2[i] + dt*w2[i]
x1 = l1*np.sin(t1)
x2 = x1 + l2*np.sin(t2)
y1 = - l1*np.cos(t1)
y2 = y1 - l2*np.cos(t2)
I know its not very neat right now, but I really just want to get it working first