Some basic principles of Hamiltonian mechanics are considered in order to provide a framework for the geometric treatment of the dynamics of \(N\)- body systems, such as molecules, clusters and complexes. The authors focus on (i) the separation of the rotational and internal energies in an arbitrary floppy \(N\)-body system and (ii) the reduction of the phase space accompanying the change from the laboratory coordinate system to the center of mass coordinate system.
The simplest case of two-body systems is considered in detail; symplectic reduction is employed to demonstrate the separation of transitional, rotational and internal energies. By examining the topology of the energy-momentum map, a unified treatment is presented of the reduction results for (i) classical dynamics of rotating and vibrating diatomic molecules and (ii) classical dynamics of atom-atom collisions.
The outlines of the relevance of the presented approach for the description of the dynamics of larger \(N\)-body systems are presented.