I extract some philosophical morals from some aspects of Lagrangian
mechanics. (A companion paper will present similar morals from Hamiltonian
mechanics and Hamilton-Jacobi theory.) One main moral concerns methodology:
Lagrangian mechanics provides a level of description of phenomena which has
been largely ignored by philosophers, since it falls between their accustomed
levels--``laws of nature'' and ``models''. Another main moral concerns
ontology: the ontology of Lagrangian mechanics is both more subtle and more
problematic than philosophers often realize.
The treatment of Lagrangian mechanics provides an introduction to the subject
for philosophers, and is technically elementary. In particular, it is confined
to systems with a finite number of degrees of freedom, and for the most part
eschews modern geometry. But it includes a presentation of Routhian reduction
and of Noether's ``first theorem''.Comment: 106 pages, no figure
