Simplified second order two-timing approximations to small amplitude nonlinear conservative oscillations

References

• Cole , J.D. and Kevorkian , J . 1963 . Uniformly valid asymptotic approximations for certain nonlinear differential equations, in Nonlinear . Differential Equations and Nonlinear Mechanics, , : 113 – 120 .
   Google Scholar
• Kevorkian , J. 1966 . Lectures in Applied Mathematics . Space Mathematics, Part III, edited by J. W. Rosser . 1966 .
   Google Scholar
• Kevorkian , J. and Cole , J.D . 1981 . Perturbation Methods in Applied Mathematics, Applied Mathematical Sciences , New York : Springer .
   Google Scholar
• Nayfeh , A.H. 1973 . Perturbation Methods , New York : Wiley .
   Google Scholar
• Morrison , J. A. 1966 . Comparison of the Modified method of averaging and the two variable expansion procedure . SIAM KEV , 8 : 66
   Web of Science ®Google Scholar
• Verhulst , F. 1983 . Asymptotic Analysis of Hamiltonian Systems in Asymptotic Analysis II , 137 – 183 . Heidelberg : Springer .
   Google Scholar
• Melvin , P.J. 1977 . On the construction of Poincare-Lindtstedt solution: the nonlinear oscillator equation . SIAM J. Appl. Math , 33 : 161
   Google Scholar