Martin Hermann - Fakulta¨t fu¨r Mathematik und Informatik, Friedrich-Schiller- Universita¨t Jena, ۰۷۷۴۳ Jena, Germany
Masoud Saravi - Department of Mathematics, Islamic Azad University Nour Branch, ۷۳۱ Nour, Iran
Hadi Ebrahimi Khah - Fakulta¨t fu¨r Mathematik und Informatik, Friedrich-Schiller- Universita¨t Jena, ۰۷۷۴۳ Jena, Germany

In this article, we investigate and apply Hamiltonianapproach method as one of the analytical approximatetechniques, for studying the strongly nonlineardynamical systems such as the motion of a rigid rodrocking back on the circular surface without slipping andthe free vibrations of an autonomous conservative oscillatorwith inertia and static-type fifth-order nonlinearities. Toillustrate the applicability and accuracy of the method, theapproximate solution results are compared with exact andnumerical solutions.

Dynamical systems Strongly nonlinear differential equations Analytical approximate techniques Hamiltonian approach method Numerical method Runge–Kutta method