The code behind @pendulum_bot Twitter bot which posts animations of a double pendulum released from a random position to swing for 30 seconds.
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 https://github.com/narimiran/double_pendulum.git
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.