ABSTRACT
The method of strained coordinates is a technique for dealing with certain types of nonuniformities which occur in asymptotic expansions. This chapter describes two related methods, namely the Lindstedt–Poincare and the Lighthill techniques. The Lindstedt–Poincare technique applies to systems which are periodic where the period of the motion is changed by a perturbation. It can be applied to various oscillators such as mechanical spring and mass systems, electrical systems and planetary motion. Lighthill's method is a generalization of the Lindstedt–Poincare method which enables strained coordinates to be applied to a far wider class of problems. The method has been found to be of particular value in the solution of the partial differential equations which occur in fluid dynamics. The asymptotic expansions are called straightforward Poincare expansions. The chapter explores how the asymptotic expansion of the solution of Duffing's equation can be rendered uniform by the Lindstedt–Poincare technique.
