Application of Higher Order Averaging

The accuracy of the results obtained in Sect. 6.3 depends heavily on the size of the system parameters. In practical applications, such as the experimental example of Chap. 9, the 0(e) error of the first-order averaging may not be sufficiently accurate for the entire range of parameters in the domain of interest. A possible way to improve the accuracy of the amplitude and frequency estimates is to extend the averaging to higher orders. 

A slightly different approach to deriving the equation of motion (of the system treated in Chap. 6) in standard form is used here. In Sect. B.l, the approximate system s equation accurate to 0 e ) is derived. The steps needed to carry out the averaging process up to the third order are presented in Sect. B.2. In Sect. B.3, a numerical example is presented that compares averaging results with numerical simulation results and actual measurements. 

---