
The normal modes in a linear mechanical system with discrete
symmetry are independent of each other. When such systems are
nonlinear, these modes are all coupled to each other. However, if a
single mode is excited, this excitation spreads to only a finite
number of other modes. This collection of modes is called a ``bush of
modes''. The dynamical behavior of a bush of modes depends on the
form of its Hamiltonian. This allows us to put bushes into
universality classes. As an example, we list the one, two, and
threedimensional bushes for all possible free molecules with
crystallographic pointgroup symmetry. (Our analysis can be applied
not only to molecules but to any macroscopic mechanical system with
point symmetry as well.) We find 363 distinct bushes that belong to
11 different classes. We give the form of the Hamiltonian for each of
those 11 classes.
