Fragmentation of particles with more than one degree of freedom

A class of fragmentation models is introduced in which the particles have more than one degree of freedom. The class of models is discussed in general terms, and analytical results are presented for a particular case of particles with two degrees of freedom. The models are compared analytically and numerically with previously solved one-dimensional models. In addition, we present exact solutions to the ``standard'' fragmentation equation when the fragmentation rate F(x,y)=xy(x+y)^α for both {α}=+1 and -1. The scaling form of these models is discussed.