Isovortical orbits of autonomous, conservative, two degreeoffreedom dynamical systems
Abstract
Conditions for the constant vorticity of an autonomous, conservative twodegreeoffreedom dynamical system are described mathematically. It is found that vorticity (the curl of velocity) is constant along the orbit if the velocity is divergencefree. A MongeAmpere differential equation is given which describes the isovortical orbits in configuration space as level curves of a scalar autonomous function. A solution for the time variable is reduced to a quadrature following the determination of the scalar function. Some selfsimilar solutions of the MongeAmpere equation under Birkhoff's (1960) oneparameter transformation group are derived for homogeneous potential functions. It is shown that Keplerian orbits belong to the class of planar isovortical flows.
 Publication:

Astrodynamics 1983
 Pub Date:
 August 1984
 Bibcode:
 1984asdy.confQ....H
 Keywords:

 Dynamic Characteristics;
 Orbit Calculation;
 Systems Analysis;
 Vorticity;
 Equations Of Motion;
 Flow Velocity;
 Kepler Laws;
 Partial Differential Equations;
 Quadratures;
 Astrodynamics