https://github.com/narimiran/double_pendulum
Animations of random double pendulums
https://github.com/narimiran/double_pendulum
animation differential-equations matplotlib numerical-methods numerics numpy python twitter twitter-bot
Last synced: 3 months ago
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Animations of random double pendulums
- Host: GitHub
- URL: https://github.com/narimiran/double_pendulum
- Owner: narimiran
- License: mit
- Created: 2018-02-13T11:05:59.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2023-01-11T22:20:16.000Z (over 2 years ago)
- Last Synced: 2025-03-15T04:46:08.649Z (3 months ago)
- Topics: animation, differential-equations, matplotlib, numerical-methods, numerics, numpy, python, twitter, twitter-bot
- Language: Python
- Homepage: https://twitter.com/pendulum_bot
- Size: 58.6 KB
- Stars: 131
- Watchers: 9
- Forks: 17
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- License: LICENSE.txt
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README
The code behind [@pendulum_bot](https://twitter.com/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:
```python
>>> 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`.
```python
>>> 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:
```python
>>> 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:
```python
>>> 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)
```
# Installation
```
git clone https://github.com/narimiran/double_pendulum.git
cd double_pendulum
```
### Dependencies
* Python 3
* numpy (running simulations)
* matplotlib (creating animations)
* ffmpeg or avconv/libavtools (saving videos)
* twython (posting Twitter updates)
# FAQ
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.
# License
[MIT License](LICENSE.txt)