SOME PECULIAR PROPERTIES OF THE DARWIN LAGRANGIAN

In the post-Galilean approximation the Lagrangians are singular on a s ubmanifold of the phase space. It is a local singularity, which differ s from the ones considered by Dirac. The dynamical properties are esse ntially peculiar on the studied singular surfaces. In the preceding pu blications,(1'2'3) two models of singular relativistic Lagrangians and the rectilinear motion of two electrons, determined by Darwin's Lagra ngian, were examined. In the present paper we study the peculiar dynam ical properties of the two-dimensional Darwin's Lagrangian. In particu lar, it is shown that the minimal distance between two electrons (the so called ''radius of electron'') appears in the two-dimensional motio n as well as in one-dimensional case. Some new peculiar properties are discovered.