I’ve got some great references and quotes here that help me explain how exactly we are able to numerically calculate the dynamics of a multibody system.

# programming

# Real-time simulations on an Arduino (double pendulum)

I got a small display compatible with my Due for christmas. And since I really wanted to see some arduino-in-the-loop simulations, I decided to use it for exactly this: real-time multibody simulations on the Ardunio and the results displayed on the tft.

# Speed comparisons for Arduino Uno/Nano, Due and Teensy 3.5

It’s been more than a year since I published my post on numerical integration on an Arduino. Since then, the post has been quite popular, recieving a steady stream of visitors (mostly via Google). When I originally wrote it, I only had an Arduino Uno at hand – since then I’ve added a couple of Nanos and lately an Arduino Due to my inventory and decided it would be interesting to do a couple of speed tests to see how they perform. The latest addition to my growing circus of microcontroller boards is a Teensy 3.5 board.

As I pointed out in the original post, numerical integration relies heavily on floating-point math – which is something the Arduino’s 8-bit processor is not particularly good at. The Due features a 32-bit processor, a clock frequency of 84 instead of 16 MHz and the possibility to use double (64 bit) instead of float (32 bit) as a data type – so I was curious to see how it would compare to the Arduino Uno. The Nano is supposed to have more or less the same characteristics as an Uno, but is a lot smaller and cheaper – see below for details.

Now added to the comparison, the Teensy 3.5 includes a 32-bit processor with 120 MHz clock speed and a FPU for speedier floating-point math.

# Object-oriented multibody simulation models in Matlab

What’s better suited for object-oriented programming (OOP) than building a simulation of a physical system? Each physical object (e.g. mass, spring etc.) can be implemented as an object and then we should be able to easily build and modify large models.

However, there are a lot of challenges to get there, including:

- How to work with classes and objects at all (if you’re like me new to OOP)?
- How to build a working object structure that adopts to the requirements of a typical ODE solver (which usually requires access to all state variables in the so-called state-space representation)
- How to design classes for different object types in a way that allows them interact with each other to calculate and transmit forces and accelerations.

Getting there turned out to be quite interesting and I finally got a simple object-oriented multibody model to simulate in Matlab and GNU Octave. This post is a wrapup of all the stuff I learned to get there.

# How to solve differential equations on an arduino with the runge-kutta method

This is just a small update on my experiments with the Arduino. I implemented the runge-kutta-method for solving a multibody system a few weeks ago. So this is a working implementation of the standard 4th-order runge-kutta ODE (ordinary differential equations) solver for the arduino platform, something I haven’t seen elsewhere.

(Note: If you are just looking for the arduino sketch, you’ll find a link at the end of this blog post. If you are wondering about related questions or have trouble adopting it to your needs, please leave a comment. Also see this post on how numerical integration of differential equations works.

Update in August 2016: See also my new post on achievable simulation rates with an Arduino Uno/Nano and Due)

My main goal was to get a better grip on simulation speeds. *Why is my simulation so slow?* is a question I’m really thinking about a lot. Since I wasn’t able to find a good example of an arduino sketch for ODE solving online, this may be interesting anyway.

# Programming advice for an engineer: Get an Arduino

Until the beginning of this year, I’ve only been coding in Matlab, GNU Octave and a few other comparable high-level 4th generation programming languages. I’ve long wanted to learn a more basic programming language which allows smaller and faster programs (more on this in another post). Basically, I wanted an answer to the question:

I’m an engineer and want to learn about programming. What can I do to get started?

It turns out one of the best answers is this: Get an Arduino.