On certain cases of determination of trajectories of plane conservative motion of a particle : PMM vol. 43, no. 6, 1979 pp. 1111–1113

A method is developed for obtaining an incomplete integral of the two-dimensional Hamilton— Jacobi equation for a particle when a particular solution that satisfies a special equation in partial derivatives is known. The equation for the trajectory of dipole particles moving with zero total energy in an arbitrary two-dimensional electrostatic field is obtain, as an example.