Equation of Motion in Standard Form

The first step toward transforming the equation of motion to a proper form for averaging is to nondimensionalize it. This is an important step to appropriately order each parameter according to its size. Expanding (6.5), yields 

To transform (6.25) into the standard form, the following change of variables is used  

Remark 6.2. The change of variable (6.27) is only allowed in situations where the RHS of (6.29) remains bounded as a approaches 0 [58]. Here, this change of variables is allowed when R is away from 0, since after expanding (6.26) using power series, we get/(a cos p, —a sin p, a) = of a, p, a) for some bounded function /forO a aQ and for sufficiently small a 1 such that N 0. FI 

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