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Perturbation method for periodic solutions of nonlinear jerk equations. (English) Zbl 1221.70017

Summary: A Lindstedt-Poincaré type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton’s method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method.

MSC:

70F10 \(n\)-body problems
70H09 Perturbation theories for problems in Hamiltonian and Lagrangian mechanics
70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics
70K60 General perturbation schemes for nonlinear problems in mechanics
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
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References:

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