The article in this week’s That’s Maths column in the Irish Times ( TM037 ) is about connections between robotics and biological systems via mechanics.
The application of mathematics in biology is a flourishing research field. Most living organisms are far too complex to be modelled in their entirety, but great progress is under way in simulating individual organs and modelling specific functions such as blood-flow and locomotion.
Biologists and mathematicians each have their own distinct jargon, and special efforts are needed to enable them to communicate. So, conferences are organised where experts from different areas try to overcome these barriers and collaborate effectively.
I recently attended such a conference in Izhevsk, about 1000 kilometres east of Moscow, entitled From Mechanical to Biological Systems – an Integrated Approach. It was a IUTAM Symposium (IUTAM is the International Union of Theoretical and Applied Mechanics), and it brought together scientists in the fields of classical mechanics, biomechanics, control theory and robotics. The main goal was to promote an integrated approach to understanding the dynamics of mechanical systems like robots on the one hand and living bodies on the other.
The main force behind the IUTAM Symposium was Alexey Borisov, a brilliant applied mathematician and author of many books and papers. Alexey has built up the Institute of Computer Science in the Udmurt State University in Izhevsk to a world-class centre. He has also spearheaded a scientific translating and publishing programme. In my presentation, I mentioned John Jellett, one-time Provost of Trinity College Dublin, President of the Royal Irish Academy and great uncle of the painter Mainie Jellett.
Jellett worked on the mathematical theory of friction, and derived an integral, or a quantity that remains constant, relating to the angular momentum of the mechanical system that I was discussing. Jellett’s book, A Treatise on the Theory of Friction, was published in Dublin in 1872. After the talk, I was greatly surprised and pleased to be presented with a Russian translation of this book, published in Izhevsk in 2009.
Accordions, Rifles and Vodka
Alexey does not fit the shy, awkward stereotype of a mathematician. He is an accomplished accordion player and we were treated to a concert of accordion music and Russian dance, arranged by him. There followed a late-night party, where we had a chance to sample the local fare. Wine and brandy were in plentiful supply, but no Kalashnikov vodka, which was surprising: Izhevsk is the home of Mikhail Kalashnikov, who died last month, and it is in this city that the infamous assault rifle, the AK-47, is manufactured.
Several symposium talks discussed flagella and cilia – whiskers and tails, if you like – used by animals for many purposes, like feeding, clearing the lungs and swimming. Robots have also been designed to use cilia for locomotion. The mechanism and modelling of robotic dynamics is a challenging area of interdisciplinary research that has thrown up several tough problems for applied mathematicians.
The robots described at the meeting were of many forms, from walking humanoids like C-3PO in Star Wars to worm-like machines for cleaning pipe networks, spherical vehicles that roll around driven by internal rotors and tiny fish-like devices that may one day swim up your arm to mend your broken heart.
Proceedings of IUTAM Symposium: Chernousko, Felix L, Alexey V Borisov, Valery V Koslov and Ivan S Mamaev, Eds, 2013: From Mechanical to Biological Systems: an Integrated Approach. Proc. IUTAM Symp., Izhevsk, 5-10 June 2012. 444pp.
Mechanical system with Jellett invariant: Peter Lynch and Miguel D Bustamante, 2013: Quaternion Solution for the Rock’n’roller: Box Orbits, Loop Orbits and Recession. Reg. & Chaotic Dyn., 18, 1-2, 166-183. DOI: 10.1134/S1560354713010127. PDF.
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Peter Lynch’s book about walking around the coastal counties of Ireland is now available as an ebook (at a very low price!). For more information and photographs go to http://www.ramblingroundireland.com/