A Classical Theory of the Collective Description

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Abstract
An elementary theory is developed of a classical treatment with the ‘Collective Motion’ of many-particle systems. The fundamental concept of collective motion can be reduced into a certain transformation property of Hamiltonian. Regarded as the dynamical variables, the continuous parameters of such a transformation describe the collective motion of the system, while the individual motions are partly suppressed by the same numbers of subsidiary conditions, or constraints, logically derived in, as the numbers of transformation parameters. Then the general procedure of formulation is illustrated; as an example, the incompressible motion with three modes can be systematically formulated. As another example, the unified treatment is performed also with the vortex motion. The digression in the approximating procedure is also presumed.

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