caa a22 4500 467987041 CHVBK 20180323112535.0 cr unu---uuuuu 170328e19900601xx s 000 0 eng 10.1007/BF00050712 doi (NATIONALLICENCE)springer-10.1007/BF00050712 Hough Michael Textron Defense Systems, 01887, Wilmington, MA, U.S.A. aut Analytic continuation of periodic orbits from equilibria of two-degree-of-freedom systems in rotating coordinates [Elektronische Daten] [Michael Hough] A new theory is formulated for the analytic continuation of periodic (and aperiodic) orbits from equilibrium solutions of a two-degree-of-freedom dynamical system in rotating coordinates:% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% acbiGab8xDayaacaGaa8xlaiaa-jdacaWFUbGaeqyXduNaa8xpaiaa% -zfadaWgaaWcbaGccaWF4baaleqaaOGaaiilaiqbew8a1zaacaGaey% 4kaSIaaGOmaiaad6gacaWG1bGaeyypa0Jaa8NvamaaBaaaleaakiaa% -LhaaSqabaGccaGGSaGabmiEayaacaGaeyypa0JaamyDaiaacYcace% WG5bGbaiaacqGH9aqpcqaHfpqDaaa!54CD!\[\dot u - 2n\upsilon = V_x ,\dot \upsilon + 2nu = V_y ,\dot x = u,\dot y = \upsilon \]Away from resonance, a family of nonlinear, normal-mode orbits defines an autonomous velocity field u(x, y), u(x, y) represented by convergent algebraic-series expansions in the two position variables. This approach is useful for determining the global structure of solution curves and nonlinear stability of normal modes using Liapunov's direct method. At resonance, the series coefficients are time dependent because stationary modes are incompatible with the equations of motion. By eliminating small divisors, explicit time dependence provides a natural transition from non-resonance to resonance cases within the same theory. Kluwer Academic Publishers, 1990 Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 49/2(1990-06-01), 151-176 0923-2958 49:2<151 1990 49 10569 https://doi.org/10.1007/BF00050712 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00050712 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hough Michael Textron Defense Systems, 01887, Wilmington, MA, U.S.A aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 49/2(1990-06-01), 151-176 0923-2958 49:2<151 1990 49 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer