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

Abstract

It is demonstrated that a suitable modification of the standard two-timing method greatly simplifies the task of establishing second order approximations to small amplitude nonlinear conservative oscillations, by reducing the number of required quadratures from ten in the standard method to merely four. Furthermore, it is shown that the remaining four quadratures are exactly those encounterd in the Lindstedt-Poincare method, so that the two-timing procedure actually reduces to the Lindstedt-Poincare one when applied to weakly nonlinear conservative systems

Keywords:

• Two-timing
• small amplitude
• conservative
• nonlinear

AMS(MOS)::

• 34E05
• 34A45