Conserved quantities can help to understand and solve the equations of motion of various dynamical systems. Lax pairs are a useful tool to ﬁnd conserved quantities of some dynami-cal systems. We give a motivated introduction to the idea of a Lax pair using examples such as the linear harmonic oscilla-tor, Toda chain and Eulerian rigid body. A key step is to write the equations in ‘Lax form’, which makes it easy to read oﬀ conserved quantities. In Part II, these ideas will be extended from systems of particles to continuum systems of ﬁelds and also given a geometric interpretation in terms of curvature..
Volume 27 | Issue 11