Abstract
The two-dimensional classical harmonic oscillator and Kepler systems possess integrals of the motion generating the algebra ofSU2. It is shown by explicit classical construction that the only two-dimensional classical system described by a HamiltonianH=T+V which is invariant underSU2 is the isotropic harmonic oscillator. The group for the Kepler system is then necessarilyO2. The meaning of this in terms of the particle orbits is discussed.
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