Introduction to Physics and Chemistry of Combustion by Michael A. Liberman

Author:Michael A. Liberman
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(7.7.8)

In fact this is just the first term in series of power expansion of and . As the modulus increases, still remaining small, subsequent higher order terms in this expansion of the third order in , forth order, etc., must be taken into account. However, since we are not interested in the exact value of the derivative , but in its time average taken over large interval of time compared to the period , all the odd-order terms, which contain the periodic factor vanish on averaging. Notice, that since , the period is small compared to the time , so that terms with the factor are fast oscillating periodic terms and they vanish over averaging. The fourth order terms, which is proportional to , does not vanish on averaging, so that we obtain

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