How numerical integration for multibody systems works

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.

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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.

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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 http://www.interactive-graphics.de/) 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.

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