How we discovered the universe

This is sooo fascinating. I mainly wrote this down for myself after reading many many wikipedia pages and added many many links. Please assume that I got a few thing’s wrong and check the links for details.

100 years ago, humanity did not know if there was anything beyond our galaxy. In telescopes, you could see small muddy blobs (nebula) and various folks, including Immanuel Kant, had long speculated that those might as well be separate galaxies, but you couldn’t be sure. And there were good reasons to doubt it – see the absolutely fascinating 1920 great debate for pro and con arguments.

It appears our universe is very old, but our knowledge on it is rather young. And both are expanding.

Continue reading “How we discovered the universe”

Dealing with complexity – a list of tools

Most of what I’m doing is managing complexity – not in the business sense but in the actual problem sense.

Engineering involes problems like: “why are these parts breaking?” (or considering the future: “Will they break and what can we do to prevent this?”). And our job as engineers is to try to break these problems down into causal effect chains and lists of options.


Then it appears to me that most engineers, developers and basically every other profession on earth are doing just the same. This made me look at other disciplines to see what’s working for whatever kind of problem.

Continue reading “Dealing with complexity – a list of tools”

References on Smooth Particle Hydrodynamics (SPH)

See …

  • here and here for physics-oriented overviews and Wikipedia for a general overview.
  • … for fluid simulations the 2003 Müller et al paper that appears to be the main reference for liquid simulation and here for a tutorial with code, a 2005 and a 2009 paper with modified algorithms and this paper here for an up-to-date overview on what happened since then.
  • here for a list of software packages and tools for SPH simulation and a second (overlapping) list of open-source packages here.
  • Here and here for videos on performance possible today on high-end systems.
  • Here for a coding challenge from Daniel Shiffman implementing fluid dynamics (haven’t watched it yet grid-based algorithm, not particle-based SPH)

I’m curious to play with this a little bit on my own, to arrive at something like this or this or maybe this (sourcecode here).

Why simulate?

Let’s define simulation as a prediction of real-world events (think of something you cannot or don’t want to measure or something you’d like to explore before actually building it). So why bother when there’s already reality to look at?

Here are a few reasons I can come up with:

  1. We want something that feels like reality (special effects in a movie or a physics engine in a video game)
  2. We want to test a physical system before actually building it (e.g. design simulations in engineering)
  3. There’s something we’d like to know we cannot easily measure (think of the inside of reactors and high-power turbines – or complex systems like sociology or medicine where we try to infer on hidden variables to estimate treatment effects)
  4. We’d like to understand something about reality and do so by building a model of it.

The last point above is a little bit obscure and I’d like to elaborate. Actually, this is my favorite reason for spending free time with simulation (in contrast to paid time at work which is all about 1-3): I’d like to learn something about reality!

Continue reading “Why simulate?”

The difference between torque and force

I remember when I was a first-year student, I had a hard time figuring out what exactly torque is. My first year of mechanics was all about static calculations and I feel torque is just so much easier to explain when you’re considering a dynamic system.

So let’s try this: Consider a body floating in free space with rocket boosters attached to it.

Force: If a rocket fires, it will exhibit a force on the body. This will make the body move (accleration = force / mass ).

The yellow rocket fires, this makes the body move to the left

Torque: If two rockets fire in opposite directions, the force will cancel out. Depending on their positions relative to each other, a torque will however be created. This will make the body rotate (rotational acceleration = torque / inertia).

Orange and red rockets fire (on the already moving body). Forces cancel out, but the body starts to rotate.

Continue reading “The difference between torque and force”

Making and forking OpenCola

I’m a huuuuge cola enthusiast, with an appetite for non-mainstream versions (most major brands just taste boring to me). So I wanted to make OpenCola for a long time and finally got around to do so.

It took me several attempts to get the recipe right, but once I did it turned out both very delicious and very easy to make. I ended up modifying the original opencola recipe for my needs and trying several versions, so here’s my summary of what did and didn’t work.

Continue reading “Making and forking OpenCola”

Bringing objects to my Processing simulation

Two years ago I’ve written a post on building an object-oriented multibody structure in Matlab. The project has since been sleeping, but since my experiments with Processing I decided to implement a comparable structure there. This means:

  • A structure that is hopefully easy to expand and modify
  • Code that is running in Java (with the possibility to port it to C++ / Arduino) that should be reasonably fast.
  • A slightly modified approach compared to my original Matlab implementation (in some cases with clear improvements)

This approach allows a very elegant interface for simulation: Adding an object is just one line of code, as is simulating one timestep:


Continue reading “Bringing objects to my Processing simulation”

Interactive multibody dynamics in Processing

Processing is a programming language / IDE built on top of Java that’s intended for simple and visual programming, making it a great tool for WYSIWYS (what you see is what you simulate, actually that is not a real term, I just made it up).

If you’re unsure what Processing is, you might want to check out either the examples on or the double-pendulum I’ve just built into it. It is a port of my code for Arduino with TFT, but with Processing, it’s cleaner and way nicer to play with!


You can find an interactive version of my program here on It also includes a general implementation of the Runge-Kutta algorithm for solving ODEs, in case this is needed (without giving any guarantee of correctness or code quality – use on your own risk).

Update 2018-02-11: I’ve just published an updated version that simulates three pendulums in parallel with different algorithms (explicit euler, symplectic euler and runge-kutta). You can find it here.

6 easy tips for creating better result plots and graphics

I’m not only a simulation nerd, I’m also a visualization nerd. My interest in formatting, layout and displays has proven to be extremely helpful in my daily work, where finding the right visual is often key to analyzing and communicating large measurement and simulation datasets. Sometimes, I also find the time to participate in fun events like the recent storytelling with data visualization challenge – which also is a good excuse to write this post on plots and visualization techniques.

So here are some simple tips to get better result plots and graphs. Most of my advice is focused on visuals for simulation results, especially in the context of large datasets and use-cases where you have to plot results frequently (like multibody simulations). This often boils down to getting the workflow right – the most beautiful visuals won’t help when creating them takes more time than what’s available.

Continue reading “6 easy tips for creating better result plots and graphics”

An Arduino Due-based Oscilloscope and Datalogger

I’ve finally built my Due and TFT into a nice housing and coded a reasonably well-working oscilloscope and datalogger for it. Here’s what I’ve learned along the way!


The oscilloscope showing analog input and digital output from an Arduino Uno powering a servo motor with the “knob” example sketch from the Arduino servo library.

Continue reading “An Arduino Due-based Oscilloscope and Datalogger”

Datalogging on Arduino (and compatibles): A comprehensive guide

I’ve used a lot of different configurations of Arduino-related gear as datalogging utilities. So here’s a comprehensive guide on what’s possible, how to set up stuff and on what you can expect regarding accuracy, battery life and logging speed.

(However, please keep in mind that I’m neither particularly skilled with electronics nor programming and other’s know a lot more on this than I do. I’m particularly grateful that Ed Mallon provided a link to this paper he coauthored with Patricia Beddows in the comments – the work and knowledge they put into it is just amazing)


My Arduino Uno with the datalogger shield both temperature and brightness sensors connected. I used a normal smartphone charger to power it for more than 3 days and placed it in this fireproof baking tray since I felt somewhat unsure about having it running unattended.

Continue reading “Datalogging on Arduino (and compatibles): A comprehensive guide”

A Kalman filter can do interesting things (like filtering poll results)

I recently learned about the Kalman filter and finally got to play around with it a little bit. Since I had a hard time figuring out how to get it to work, here’s a practical (but yet general) introduction with examples:

A Kalman filter works by matching a simulation model and measured data. For each data point, an estimation of the simulation model’s internal state is computed based on the estimate of the previous state. This works with noisy data and limited measurement signals (e.g. a model with 10 state variables but only 2 measurement signals, although there are obvious limitations here (the more and the better the sensor data, the better the results should be – there’s also some limit on observability).

So we have this interesting tool which does all these different things:

  • filtering noisy data, while taking knowledge (or assumptions) on the underlying dynamics into account
  • merge data from several different sensors into one signal (typical application: combine GPS and acceleration sensor data into one accurate position signal)
  • offer a prediction of a system’s future state
  • estimate internal parameters of a system (say a spring stiffness based on measured oscillations)

Another interesting use is that we might try two different simulation models on the same measurement and check which one does a better job at synchronizing to the measurement (I’ll do this in a very simple example below).

Continue reading “A Kalman filter can do interesting things (like filtering poll results)”

Speed comparisons for Arduino Uno/Nano, Due, Teensy 3.5 and ESP32

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. (Update May 2019: Added a ESP32 dev 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.

Continue reading “Speed comparisons for Arduino Uno/Nano, Due, Teensy 3.5 and ESP32”

Raspberry pi: Video and Audio recording and streaming guide

I’ve spent some time on setting up audio and video streaming on my raspberry pi (mostly used as a baby monitor right now). While there are great ressources out there, it took me a lot of effort to find them and put everything together. So here’s a handy list of instructions if you want to:

  • Record and stream audio
  • Record and stream both audio and video into one file
  • Are just looking for an introduction into the topic.

Continue reading “Raspberry pi: Video and Audio recording and streaming guide”

DIY glowing lamp with shifting colors (Arduino-based and interactive)

This post is not really about multibody dynamics. Instead of simulating stuff, I’ve actually built something: A glowing, more-or-less-interactive lamp.

We are awaiting our first child and with all the things we bought (mostly used), there was a small, adorable lamp. Unfortunately, it had some weird-looking electrics inside (both looking very old and labeled for 120V – so it wouldn’t work with our 230V here in Germany), so we decided to remove all cables and replace them with LEDs. Actually, WE just decided not to use the existing cables and then I talked my wife into letting me build something with an Arduino.

So I hooked up the lamp with a digital LED-stripe – I found one that came with digitally-adressable LEDs and used the Adafruit Neopixel library to adress those. Now there are 24 RGB-LEDs inside the lamp which I can control direct with the Arduino.

Continue reading “DIY glowing lamp with shifting colors (Arduino-based and interactive)”

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.

Update: There is now also a newer post I’ve just written on a comparable multibody simulation structure in Processing / Java.

Continue reading “Object-oriented multibody simulation models in Matlab”

Impulse-based dynamics: A simple and fast way to simulate contacts and constraints

So far, I’ve mostly been working on rotational mechanics – multibody models where each mass only has one rotational degree of freedom and two state variables (angle and angular velocity). Every now and then, I use some commercially available tools to simulate more complex 2d and 3d models – often being surprised by how slow simulation is. At the same time, I’ve been wondering a lot:

  • how I’d actually model these problems by hand – especially when additional boundary conditions and/or contacts are involved.
  • why some video games seem to be able to include complex dynamics with detailed contact and collisions involved, simulating in real time (while commercial multibody simulation often takes hours to calculate a few seconds of dynamic behavior).

An important answer to these questions is the topic of impulse-based dynamics. I stumbled upon it in some amazing literature from Prof. Jan Bender (see and so far I’ve been experimenting a bit with the method myself. This post today features a small and practical introduction to modelling boundary conditions in impulse-based mechanics.

Continue reading “Impulse-based dynamics: A simple and fast way to simulate contacts and constraints”