Motion on two-dimensional manifolds in rotating coordinates

Details Motion on two-dimensional manifolds in rotating coordinates Motion on two-dimensional manifolds in rotating coordinates

Jun 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990cemda..50..143h&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 50, Issue 2, pp.143-164

Astronomy and Astrophysics

Astronomy

Rotating Coordinates, Velocity Field, Integral Curves

Scientific paper

The two degree-of-freedom system in rotating coordinates: udot - 2nv = V x, vdot + 2nu = V y, xdot = u, ydot = v and its Jacobi integral define a time-dependent velocity field on a differentiable, two-dimensional manifold of integral curves. Explicit time dependence is determined by the dynamical system, coordinate frame, and initial conditions. In the autonomous cases, orbits are level curves of an autonomous function satisfying a second-order, quasi-linear, partial differential equation of parabolic type. Important aspects of the theory are illustrated for the two-body problem in rotating coordinates.

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