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PIPES CONVEYING FLUID: NONLINEAR AND CHAOTIC DYNAMICS 299

These equations are rendered dimensionless with the aid of relations (5.68) and the
following additional ones:

(5.73)

5.4 METHODS OF SOLUTION AND ANALYSIS
With a few rare exceptions,S no general analytical solutions of the nonlinear equations
of motion are possible. Therefore, recourse has to be taken to specialized analytical,
semi-analytical and numerical techniques. Here, the classification proposed by Nayfeh

+With some corrections vis-&vis Bajaj & Sethna (1982a) - Bajaj (1998).
*For example, for the nonlinear equation of a simple pendulum, via elliptic integrals.