import torch

dt = torch.tensor([0.02]).double()
m = torch.tensor([1.0]).double()
l = torch.tensor([1.0]).double()
g = torch.tensor([9.80665]).double()
pi = torch.tensor([3.14159265359]).double()

def pendulom (x, u):
    theta = torch.atan2(x[0], x[1])
    theta_dot = x[2]
    next_theta = theta + theta_dot*dt

    theta_dot_dot = -3.0 * g / (2 * l) * tr.sin(theta + pi)
    theta_dot_dot += 3.0 / (m * l**2) * u.double()
    next_theta_dot = theta_dot + theta_dot_dot * dt

    return torch.stack((
                        torch.sin(next_theta),
                        torch.cos(next_theta),
                        next_theta_dot
                       ),0)

x = tr.tensor([0., 1., 0.],dtype=torch.float64, requires_grad=True)
u = tr.tensor([-1.0], dtype=torch.float64, requires_grad=True)
y = pendulom(x,u)
y.backward(torch.ones_like(y))
x.grad

output:
tensor([1.2942, 0.0000, 1.0200], dtype=torch.float64)