Abstract
A systematic and detailed discussion of the ‘gravitational’ spring-pendulum problem is given for the first time. A procedure is developed for the numerical treatment of non-integrable dynamical systems which possess certain properties in common with the gravitational problem. The technique is important because, in contrast to previous studies, it discloses completely the structure of two-dimensional periodic motion by examining the stability of the one-dimensional periodic motion. Through the parameters of this stability, points have been predicted from which the one-dimensional motion bifurcates into two-dimensional motion. Consequently, families of two-dimensional periodic solutions emanated from these points are studied. These families constitute the generators of the mesh of all the families of periodic solutions of the problem.
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Kazantzis, P.G. Numerical treatment of non-integrable dynamical systems. Astrophys Space Sci 61, 287–316 (1979). https://doi.org/10.1007/BF00640533
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DOI: https://doi.org/10.1007/BF00640533