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Contents: Background | Installation | Running | Contributing |

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Background

Welcome to SkyDy—a Dynamics package for Python built by me, Scott Kyle.

The purpose of this repository is to provide a way to programmatically define an inter-connected mechnical system (ICMS)—a collection of rigid bodies—to ultimately determine its:

• coordinate system;
• forward kinematic maps;
• kinetic and potential energy;
• kinetic energy (Riemannian) metric;
• generalised forces;
• equations of motion;
• forced and unforced equilibria.

The idea is to have a fully integrated way to define and describe ICMS, and produce useful content. Note, we refer the user to Geometric Control of Mechanical Systems (Bullo & Lewis) for definitions and descriptons used throughout.

ICMS are typically "simple" to scribble down on a piece of paper, yet notoriously "difficult" to model correctly. Even with two bodies, the book-keeping and accounting on the rotation matrices alone renders the modelling task cumbersome and error prone. This repository is here to (help) solve that.

The goal is to be able to take a schematic drawing from paper, and by methodically using code, define the ICMS. The output of this effort can be one, or many of the following:

1. A diagram of the ICMS.
2. A latex document (and PDF), deriving equations of motion.
3. A symbolic representation, that can be used a starting point for running simulations.

This repository relies on the principle that any system is simply a collection of independent bodies connected, via joints, in different geometric configurations. As such, the mainstays of this repository are the following classes:

• Body: a collection of particles that has a mass, and some dimensions (length, width and height), and has six degrees of freedom (DOFs).
• Joint: a common location for two bodies to interact, and a description of how the bodies can move relative to each other. A Joint allows motion in certain directions (DOFs) and/or enforces constraints. Thus, a Joint dictates the spatial coordinates (or variables) each body will contribute to the ICMS.
• Connection: defined by an input and output Body, and a Joint. Since (by construction) the location of the joint is defined in both the input body and output body's coordinate frames, the configuration of the output Body can be written in terms of the input Body. A connection is also where we enforce the constraints of the Joint, which ultimately dictates how the output Body moves in the coordinate frame of the input Body.
• BodyCoordindate: defines an (x, y, z) triple in the respective body coordinate frame, from its centre of mass. As we connect bodies to one another, we start to translate and rotate these coordinates by the position and rotation matrices (Configuration) of each Body.
• MultiBody: a sequence of Connections. If we are diligent with our definitions of coordinates, bodies and joints, the creation of a MultiBody is straightforward.
• Ground: every system needs reference to a global, or fixed coordinate frame. This is defined as the Ground. It does not translate. It does not rotate. It is our origin (0, 0, 0). Every MultiBody needs one.

For this methodology, all definitions and descriptions are done in a Body's coordinate frame.

Installation & Usage

Installation

1. Build from this repository:
   1. Build a local copy of the package (see note):
      1. git clone https://github.com/smkyle90/skydy.git
      2. cd skydy
      3. pip install --upgrade .
   2. Using Docker:
      1. git clone https://github.com/smkyle90/skydy.git
      2. cd skydy
      3. make build
2. Using pip and PyPi (see note):
   1. pip install skydy.

Note: For 1.1 and 2.1, OS level dependencies include python3-tk and pdflatex.

Usage

We encourage the reader to review the examples folder for some basic examples. There are useable .py files in the python directory, as well as interative notebooks in notebooks. The collection of examples are the simplest, yet most common, systems this modelling methodology can be used on, and include:

1. A one-dimensional cart that moves in the x-coordinate.
2. A one-dimensional pendulum that rotates about an axis.
3. A cart-pendulum—a combination of the two systems above.
4. A hovercraft—an object that can move in two-dimensions and rotate.
5. A double pendulum.

For step-by-step development, the user is encouraged to run their code in an interactive notebook. This will leverage the power of Sympy and the skydy process. The Docker image associated with this repository has Jupyter installed. To enter an interactive session, simply run jupyter notebook --allow-root from the container and copy and paste the address the terminal provides into your browser of choice.

Documentation

Skydy documentation can be found here on Read The Docs! The docs are aligned with the latest Github release.

Running

For this repository to function as intended, a few tools have been provided to ensure the application can be containerised.

Makefile

The content of the Makefile should only be modified if the standard behaviour is not achieved using the default. Standard commands are as follows:

Command	Action	Image Tag (local and remote)
make run	Runs a local image	Git commit's tag, otherwise latest

Scripts

The scripts folder must maintain the following, which are indirectly run from the Makefile in the root directory. The build script is customizable per the application, but it must build a local image of the application. The run script Thruns the container without local screen priviledged. The dev script allows the user to use the screen of their local machine.

Script	Inputs	Output
build.sh	NAME TAG	Application image is created locally, tagged with input args
run.sh	NAME TAG	Application image is run locally
dev.sh	NAME TAG	Application image is run locally, with screen priviledsges for plotting and development purposes

Developing & Contributing

The guidelines for contributing are laid out here. All members of the team have write access.

TODO

What I want to get done:

• Documentation (Completed June 13, 2021. Docstrings added and infrastructure for Read The Docs & Sphinx autodocs. Release v0.0.2.)
• Decent Documentation (Release v0.0.3.)
• Thorough Documentation
• Prettier Latex printing
• Add mass data to a Body for MassMatrix and InertiaMatrix objects
• Kinematically constrained objects
• Translational and rotational springs and dampers
• Faster Forward Kinemtics
• Dig into sympy.physics.mechanics and their Lagrangian capabilties
• Rotating forces
• Simulations
• Systems analysis, including:
  • Stability analysis (Release v0.0.3)
  • Controllability (both Linear and Nonlinear) (Release v0.0.3)
• Control Design
• Decrease the size of the Docker image
• Add an image to Docker hub

Development Environment

• Install Docker for creating a nice virtual container to run in.
• See Running.

Testing

No untested code will be allowed to merge onto Master. A 90% coverage and test passing report is required for all Master PRs.

Using PyTest

This library uses pytest for testing. To run the full test suite use the command pytest tests/ --cov=skydy --cov-report=html.

Take note of the marks in pytest.ini. To run specific tests, say only the "rigidbody" module, run pytest tests/ --cov=skydy --cov-report=html -m rigidbody.

One can use the args -vv -s to get detailed print outs during testing, i.e., pytest tests/ --cov=skydy --cov-report=html -vv -s

Code Style

Code style is handled and enforced with Black, Flake8 and some additional stylers and formatters. A pre-commit hook is provided with this repository so that all code is automatically kept consistent. If there are any issues with formatting, please submit a formal PR to this repository.

Docstrings will be formatted according to the Google docstring formatting, and as best as possible, styled as per the PEP 8 style guide.