The motion in the field of a rotationally symmetrical potential - The contour of the orbit and of the folds of the field of directions

Details The motion in the field of a rotationally symmetrical potential - The contour of the orbit and of the folds of the field of directions The motion in the field of a rotationally symmetrical potential - The contour of the orbit and of the folds of the field of directions

Jun 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988azh....65..648a&link_type=abstract

Astronomicheskii Zhurnal (ISSN 0004-6299), vol. 65, May-June 1988, p. 648-652. In Russian.

Mathematics

Dynamical Systems

Dynamical Systems, Orbits, Potential Fields, Trajectory Analysis, Contours, Partial Differential Equations, Rotating Environments

Scientific paper

The equation for the ratio of the second-order gradient along the normal to the trajectory of the field of directions to the cube of the first-order gradient is obtained from the contour of the orbit and from contours of folds of the direction field. Together with the equation for the curvature of the contour, it permits to construct the complete pattern of contours without solving the equations of motion.

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