Initial conditioned solutions of a second-order nonlinear conservative differential equation with a periodically varying coefficient |
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Authors: | Lucas Pun |
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Institution: | Laboratoire d''Électronique Appliquée Facalté des Sciences de l'' Université de Bordeaux, Talence, France |
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Abstract: | The exact solution of the equation where d, d' and w are positive constants, and ?(wt) is a rectangular periodic function of time is discussed. The equation describes approximately the transversal movement of a particle in an alternating gradient accelerator. The exact solution is obtained in the form of a composite recurrent relation containing five particular solutions. Each of these solutions corresponds to a specific well-defined area of the phase plane of the initial conditions. The dynamical behaviour and the stability of the movement are examined analytically. |
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