Motion on two-dimensional manifolds in rotating coordinates |
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| Authors: | Michael E Hough |
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| Institution: | (1) Textron Defense Systems, 01887 Wilmington, MA, U.S.A. |
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| 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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| Keywords: | Rotating coordinates velocity field integral curves |
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