These being lecture notes
for a summer school, one should not seek original material in them. Rather, the most
one could hope to find would be the insight arising from incorporating a unified
approach (based on reduction by symmetry of Hamilton’s principle) with some
novel applications. I hope the reader will find insight in the lecture notes,
which are meant to be informal, more like stepping stones than a proper
path.
Keywords
geometric mechanics, Lie group invariant
variational principles, Camassa–Holm equation
