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Awesome Open Source

Double pendulum

The code behind @pendulum_bot Twitter bot which posts animations of a double pendulum released from a random position to swing for 30 seconds.


Basic usage

To create an animation of a random double pendulum:

>>> from simulation import create_random_example, simulate
>>> from animations import single_animation
>>> rand_ex = create_random_example()
>>> results = simulate(rand_ex)
>>> single_animation(results, rand_ex)

The animation is saved as .mp4 video in animations subdirectory.

To create an animation and post it on Twitter, a valid API key is needed, and should be stored in api_key.txt.

>>> from tweet_it import new_tweet
>>> new_tweet() # creates a new animation of random double pendulum
# or
>>> new_tweet('existing_file', 'My custom Twitter status')

To create double pendulum with the exact values for initial conditions:

>>> from pendulum import Pendulum, DoublePendulum
>>> p1 = Pendulum(m=2.7, x=2.5, y=3.7, u=0, v=0)
>>> p2 = Pendulum(m=3.1, x=0.2, y=6.3, u=0, v=0)
>>> dp = DoublePendulum(p1, p2)

To create multiple pendulums with slight perturbations of initial conditions to observe chaotic behaviour:

>>> from simulation import create_random_example, create_perturbations, simulate_multiple_examples
>>> from animations import multi_animation
>>> rand_ex = create_random_example()
>>> perturbed = create_perturbations(10, rand_ex, amount=1e-5)
>>> results = simulate_multiple_examples(perturbed)
>>> multi_animation(results, rand_ex)



git clone
cd double_pendulum


  • Python 3
  • numpy (running simulations)
  • matplotlib (creating animations)
  • ffmpeg or avconv/libavtools (saving videos)
  • twython (posting Twitter updates)



Q: Why do you use Cartesian coordinates? I prefer polar coordinates.

A: The initial task I was given was to implement double pendulum as DAE system in Cartesian coordinates. The idea for animations and Twitter bot came later, and Cartesian coordinates remained.

Q: Which Runge-Kutta methods can I use?

A: Any of these:

  • Forward Euler (Euler)
  • Explicit midpoint (ExplicitMidpoint)
  • Ralston's method (Ralston)
  • Kutta's 3rd order method (Kutta3)
  • the Runge-Kutta 4th order method (RK4)
  • Runge-Kutta-Fehlberg (RKF)
  • Cash-Karp (Cash-Karp)
  • Dormand-Prince method (DOPRI5)

Q: Why can't I use implicit Runge-Kutta methods?

A: Implicit methods require different solving method (solving a system of non-linear equations). This is not (yet) implemented.

Q: Is there any damping/friction?

There is no damping and no friction. The only force acting on the system is gravity.

Q: Couldn't all/some of this be done simpler?

A: Probably.



MIT License

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