In the published version of the paper:
the following error has occurred:
Peter W. Michor, David Mumford:
An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach.
Applied and Computational Harmonic Analysis 23 (2007), 74-113. doi:10.1016/j.acha.2006.07.004.
The horizontal geodesic equation in 3.6 should have an overall - in front of
a_t = - \frac.....
The version on Peter Michor's homepage has been corrected.