Classical integrable many-body systems disconnected with semi-simple Lie algebras

The review of the results in the theory of integrable many-body systems disconnected with semisimple Lie algebras is done. The one-dimensional systems of light Calogero–Sutherland–Moser particles interacting with one particle of infinite mass located at the origin are described in detail. In some cases the exact solutions of the equations of motion are obtained. The general theory of integration of the equations of motion needs the methods of algebraic geometry. The Lax pairs with spectral parameter are constructed for this purpose. The theory still contains many unsolved problems.