Gradient of the direction field along the normal to a trajectory

Details Gradient of the direction field along the normal to a trajectory Gradient of the direction field along the normal to a trajectory

Oct 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976azh....53.1106a&link_type=abstract

Astronomicheskii Zhurnal, vol. 53, Sept.-Oct. 1976, p. 1106-1109. In Russian.

Astronomy and Astrophysics

Astronomy

2

Gradients, Orbit Calculation, Trajectory Analysis, Equations Of Motion, Orbital Mechanics, Partial Differential Equations, Polynomials

Scientific paper

The paper obtains the analytical form of the gradient of the direction field along a normal to a trajectory which depends on the local properties of the potential. The number of roots of the denominator is equal to the number of orbital contours and contours of the folds of the field of velocity directions crossing the point (R, z) at the corresponding values of the third integral of motion. When the root of the denominator is the root of the numerator also, then the point (R, z) is crossed by a stable periodic orbit.

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