Analytic continuation of quasi-periodic orbits from non-linear periodic modes |
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Authors: | Michael E Hough |
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Institution: | (1) Textron Defense Systems, 01887 Wilmington, MA, USA |
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Abstract: | A new theory is formulated for the analytic continuation of quasi-periodic orbits from non-linear, periodic modes of a two degree-of-freedom system in rotating coordinates. Formal solutions of the equations of motion are developed in series expansions, with the non-linear modes as reference solutions. Conditions are determined on the existence and boundedness of the time-dependent coefficients of the velocity field. Boundedness properties of the orbits are specified by an orbit function derived from the Jacobi integral. |
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Keywords: | Perturbation theory quasi-periodic motion non-linear stability |
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