PyDy, short for Python Dynamics, is a tool kit written in the Python programming language that utilizes an array of scientific programs to enable the study of multibody dynamics. The goal is to have a modular framework and eventually a physics abstraction layer which utilizes a variety of backends that can provide the user with their desired workflow, including:
- Model specification
- Equation of motion generation
- Simulation
- Visualization
- Publication
We started by building the SymPy mechanics package which provides an API for building models and generating the symbolic equations of motion for complex multibody systems. More recently we developed two packages, pydy.codegen and pydy.viz, for simulation and visualization of the models, respectively. This Python package contains these two packages and other tools for working with SymPy mechanics. The remaining tools currently used in the PyDy workflow are popular scientific Python packages such as NumPy, SciPy, IPython, and matplotlib (i.e. the SciPy stack) which provide additional code for numerical analyses, simulation, and visualization.
PyDy has hard dependencies on the following software:
PyDy has optional dependencies on these packages:
The examples may require these dependencies:
It's best to install the SciPy Stack dependencies using the instructions provided on the SciPy website. We recommend the conda package manager and the Anaconda distribution for easy cross platform installation.
Once the dependencies are installed, the package can be downloaed from PyPi:
$ wget https://pypi.python.org/packages/source/p/pydy/pydy-0.2.1.tar.gz
and extracted and installed[#]:
$ tar -zxvf pydy-0.2.1.tar.gz
$ cd pydy-0.2.1
$ python setup.py install
Or if you have the pip package manager installed you can simply type:
$ pip install pydy
This is an example of a simple one degree of freedom system: a mass under the influence of a spring, damper, gravity and an external force:
/ / / / / / / / /
-----------------
| | | | g
\ | | | V
k / --- c |
| | | x, v
-------- V
| m | -----
--------
| F
V
Derive the system:
from sympy import symbols
import sympy.physics.mechanics as me
mass, stiffness, damping, gravity = symbols('m, k, c, g')
position, speed = me.dynamicsymbols('x v')
positiond = me.dynamicsymbols('x', 1)
force = me.dynamicsymbols('F')
ceiling = me.ReferenceFrame('N')
origin = me.Point('origin')
origin.set_vel(ceiling, 0)
center = origin.locatenew('center', position * ceiling.x)
center.set_vel(ceiling, speed * ceiling.x)
block = me.Particle('block', center, mass)
kinematic_equations = [speed - positiond]
force_magnitude = mass * gravity - stiffness * position - damping * speed + force
forces = [(center, force_magnitude * ceiling.x)]
particles = [block]
kane = me.KanesMethod(ceiling, q_ind=[position], u_ind=[speed],
kd_eqs=kinematic_equations)
kane.kanes_equations(forces, particles)
Create a system to manage integration and specify numerical values for the constants and specified quantities. Here, we specify sinusoidal forcing:
from numpy import array, linspace, sin
from pydy.system import System
sys = System(kane,
constants={mass: 1.0, stiffness: 1.0,
damping: 0.2, gravity: 9.8},
specifieds={force: lambda x, t: sin(t)},
initial_conditions={position: 0.1, speed: -1.0})
Integrate the equations of motion under the influence of a specified sinusoidal force:
sys.times = linspace(0.0, 10.0, 1000)
y = sys.integrate()
Plot the results:
import matplotlib.pyplot as plt
plt.plot(sys.times, y)
plt.legend((str(position), str(speed)))
plt.show()
The documentation is hosted at http://pydy.readthedocs.org but you can also build them from source using the following instructions.
To build the documentation you must install the dependencies:
To build the HTML docs, run Make from within the docs
directory:
$ cd docs
$ make html
You can then view the documentation from your preferred web browser, for example:
$ firefox _build/html/index.html
This package provides code generation facilities. It generates functions that can numerically evaluate the right hand side of the ordinary differential equations generated with sympy.physics.mechanics with three different backends: SymPy's lambdify, Theano, and Cython.
The models module provides some canned models of classic systems.
The System module provides a System
class to manage simulation of a single system.
This package provides tools to create 3D animated visualizations of the systems. The visualizations utilize WebGL and run in a web browser. They can also be embedded into an IPython notebook for added interactivity.
The source code is managed with the Git version control system. To get the latest development version and access to the full repository, clone the repository from Github with:
$ git clone https://github.com/pydy/pydy.git
You should then install the dependencies for running the tests:
It is typically advantageous to setup a virtual environment to isolate the development code from other versions on your system. There are two popular environment managers that work well with Python packages: virtualenv and conda.
The following installation assumes you have virtualenvwrapper in addition to virtualenv and all the dependencies needed to build the various packages:
$ mkvirtualenv pydy-dev
(pydy-dev)$ pip install numpy scipy cython nose theano sympy ipython[all]
(pydy-dev)$ pip install matplotlib # make sure to do this after numpy
(pydy-dev)$ git clone git@github.com:pydy/pydy.git
(pydy-dev)$ cd pydy
(pydy-dev)$ python setup.py develop
Or with conda:
$ conda create -n pydy-dev setuptools numpy scipy ipython ipython-notebook cython nose theano sympy matplotlib
$ source activate pydy-dev
(pydy-dev)$ git clone git@github.com:pydy/pydy.git
(pydy-dev)$ cd pydy
(pydy-dev)$ python setup.py develop
The full Python test suite can be run with:
(pydy-dev)$ nosetests
For the Javascript tests the Jasmine and blanket.js libraries are used. Both of these libraries are included in pydy.viz with the source. To run the Javascript tests:
cd pydy/viz/static/js/tests && phantomjs run-jasmine.js SpecRunner.html && cd ../../../../../
Run the benchmark to test the n-link pendulum problem with the various backends:
$ python bin/benchmark_pydy_code_gen.py <max # of links> <# of time steps>
These are various related and similar Python packages:
- https://github.com/cdsousa/sympybotics
- https://pypi.python.org/pypi/Hamilton
- https://pypi.python.org/pypi/arboris
- https://pypi.python.org/pypi/PyODE
- https://pypi.python.org/pypi/odeViz
- https://pypi.python.org/pypi/ARS
- https://pypi.python.org/pypi/pymunk
If you make use of PyDy in your work or research, please cite us in your publications or on the web. This citation can be used:
Gilbert Gede, Dale L Peterson, Angadh S Nanjangud, Jason K Moore, and Mont Hubbard, "Constrained Multibody Dynamics With Python: From Symbolic Equation Generation to Publication", ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2013, 10.1115/DETC2013-13470.
If you have any question about installation, usage, etc, feel free send a message to our public mailing list or visit our Gitter chatroom.
If you think there’s a bug or you would like to request a feature, please open an issue on Github.
- Overhauled the code generation package to make the generators more easily extensible and to improve simluation speed. [PR #113]
- Added a new System class and module to more seamlessly manage integrating the equations of motion.
- When using older SymPy development versions with non-PEP440 compliant version identifiers, setuptools < 8 is required. [PR #166]
- Development version numbers are now PEP 440 compliant. [PR #141]
- Introduced pull request checklists and CONTRIBUTING file. [PR #146]
- Introduced light code linting into Travis. [PR #148]
- Unbundled unnecessary files from tar ball.
- Merged pydy_viz, pydy_code_gen, and pydy_examples into the source tree.
- Added a method to output "static" visualizations from a Scene object.
- Dropped the matplotlib dependency and now only three.js colors are valid.
- Added joint torques to the n_pendulum model.
- Added basic examples for codegen and viz.
- Graceful fail if theano or cython are not present.
- Shapes can now use sympy symbols for geometric dimensions.