Abstract
A class of second-order equation fields which contains the equations of motion of the Kepler and charge monopole problems is considered. In particular, the problems of the existence of a second integral of motion quadratic in momenta besides the energy is investigated and completely solved. A subclass of systems is exhibited which have a Runge-Lenz-type vector, but it is shown that the monopole system itself has no second (time-independent) quadratic integral of motion.
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