Parametrically driven pendulum and exact solutions |
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| Authors: | W. -H. Steeb N. Euler |
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| Affiliation: | (1) Department of Applied Mathematics and Nonlinear Studies, Rand Afrikaans University, 2000 Johannesburg, South Africa |
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| Abstract: | The parametrically driven pendulumx +f1(t) x +f2(t) sinx = 0 cannot be solved in closed form for arbitrary functionvsf1,f2. We apply the Painlevé test to obtain the constraint on the functionsf1, andf2 for which the equation passes the test. The constraint onf1, andf2, a differential equation whichf1 andf2 obey, is discussed and solutions are given. The third Painlevé transcendent plays a central role. |
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