Hamiltonʼs principle of mechanics has special advantages as the beginning point for approximations. First, it is extremely succinct. Secondly, it easily accommodates moving disconnecting fluid boundaries. Thirdly, approximations – however strong – that maintain the symmetries of the Hamiltonian will automatically preserve the corresponding conservation laws. For example, Hamiltonʼs principle allows useful analytical and numerical approximations to the equations governing the motion of a homogeneous rotating fluid with free boundaries.