Hamiltonian approach to nonlinear oscillators

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Nonlinear vibration analysis of functionally graded beams considering the influences of the rotary inertia of the cross section and neutral surface position (2018, methodology): “(10) By using Hamilton’s principle and the variational principle (He, 2002, 2010; Younesian et al., 2010), the equations of motion can be derived as ∂Nx ∂x = I0Ü − I1 ∂Ẅ ∂x ; ∂2Mx ∂x2 + ∂ ∂x ( Nx ∂W ∂x ) = I0Ẅ + I1 ∂Ü ∂x − I2 ∂2Ẅ ∂x2 , (11) where dot-superscript convention indicates the di…”
The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators (2019, unknown): “0 1 2 A(2)x(2)sin(2)xt FðAcosxtÞ dt (30)”
Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review (2012, methodology): “Recently, He [111]has proposed the Hamiltonian approach to 899 overcome the shortcomings of the energy balance method.”