As a modern subject, geometric mechanics has its roots in four works written in the 1960s. These were by Vladimir Arnold (1966), Stephen Smale (1970) and Jean-Marie Souriau (1970), and the first edition of Abraham and Marsden 's Foundation of Mechanics (1967). Arnold's fundamental work showed that Euler's equations for the free rigid body are the equations for geodesic flow on the rotation group SO(3) and carried this geometric insight over to the dynamics of ideal fluids, where the rotation group is replaced by the group of volume-preserving diffeomorphisms. Smale's paper on Topology and Mechanics investigates the conserved quantities arising from Noether's theorem when a Lie group of symmetries acts on a mechanical system, and defines what is now called the momentum map (which Smale calls angular momentum), and he raises questions about the topology of the energy-momentum level surfaces and the effect on the dynamics. In his book, Souriau also considers the conserved quantities arising from the action of a group of symmetries, but he concentrates more on the geometric structures involved (for example the equivariance properties of this momentum for a wide class of symmetries), and less on questions of dynamics.