Extension of the Hamiltonian approach with general initial conditions

• Autorzy: Navarro H. A. , Cveticanin L.

Identyfikatory

DOI

10.15632/jtam-pl.56.1.255

• Języki publikacji: EN

Abstrakty

EN

In this paper, the Hamiltonian approach is extended for solving vibrations of nonlinear conservative oscillators with general initial conditions. Based on the assumption that the derivative of Hamiltonian is zero, the frequency as a function of the amplitude of vibration and initial velocity is determined. A method for error estimation is developed and the accuracy of the approximate solution is treated. The procedure is based on the ratio between the average residual function and the total energy of the system. Two computational algorithms are described for determining the frequency and the average relative error. The extended Hamiltonian approach presented in this paper is applied for two types of examples: Duffing equation and a pure nonlinear conservative oscillator.

Słowa kluczowe

EN

nonlinear dynamics; Hamiltonian approach; error estimation

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2018
• Tom: Vol. 56 nr 1
• Strony: 255--267
• Opis fizyczny: Bibliogr. 28 poz., rys., tab.

Twórcy

autor

Navarro H. A.

• Escola de Engenharia de São Carlos, Universidade de São Paulo, São Paulo, Brazil

autor

Cveticanin L.

• Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).