Isovortical orbits of autonomous, conservative, two degree-of-freedom dynamical systems
Abstract
Conditions for the constant vorticity of an autonomous, conservative two-degree-of-freedom dynamical system are described mathematically. It is found that vorticity (the curl of velocity) is constant along the orbit if the velocity is divergence-free. A Monge-Ampere 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 self-similar solutions of the Monge-Ampere equation under Birkhoff's (1960) one-parameter 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