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Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms. (English) Zbl 1225.34044
Summary: Hamiltonian Approach (HA) is applied to obtain the analytical approximate solution of the nonlinear oscillators with Rational and Irrational Elastic Terms. Periodic solutions are analytically verified and consequently the relationship between the natural frequency and the initial amplitude is obtained in an analytical form. A comparison of the period of oscillation and obtained solutions with the exact results illustrates that the Hamiltonian approach is very effective and quite accurate for nonlinear equations.

MSC:
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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