Abstract
The two degree-of-freedom system in rotating coordinates: \.u − 2nv = V x, \.v + 2nu = V y, \.x = u, \.y = 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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References
Hough, M. E.: 1986, Celest. Mech., 39, 249.
Hough, M. E.: 1987, Celest. Mech., 40, 111.
Hough, M. E.: 1988, Celest. Mech., 44, 1.
Hough, M. E.: 1991, Celest. Mech., 49, 151.
Jacobi, C.: 1836, Compte Rendu des Seances, 3, 59.
Szebehely, V.: 1967, Theory of Orbits, Academic Press, N.Y.
Szebehely, V. and Broucke, R.: 1981, Celest. Mech., 24, 23.
Whittaker, E.: 1961, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge University Press, Fourth Edition.
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Hough, M.E. Motion on two-dimensional manifolds in rotating coordinates. Celestial Mech Dyn Astr 50, 143–164 (1990). https://doi.org/10.1007/BF00051047
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DOI: https://doi.org/10.1007/BF00051047