Potentials having two orthogonal families of curves as trajectories

Details Potentials having two orthogonal families of curves as trajectories Potentials having two orthogonal families of curves as trajectories

Jul 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999cemda..74..199p&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 74, Issue 3, p. 199-210 (1999).

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Inverse Problem, Joukovsky'S Formula, Compatibility, Isothermal Curves, Inverse Problem, Joukovsky'S Formula, Compatibility, Isothermal Curves

Scientific paper

We study, using the tool of Joukovsky’s orthogonal coordinates, the determination of the potentials having two families of orthogonal trajectories. We show for compatible cases the existence and the uniqueness, up to a constant factor, of the solution. We note the importance of the ‘isothermal’ nets of curves. We study as an example the net of geometrically similar conic curves and orthogonal trajectories.

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