Abstract
A harmonic balance method is presented in which Jacobi elliptic functions are used in the trial solution instead of circular functions to obtain approximate periodic solutions of the oscillator x ̈ + F ( x, dot x ) = 0 . Conditions for the method to work well are the usual ones of the current method of harmonic balance, and that x(t) must pass through zero. The procedure for obtaining a higher order approximation is described, and in particular two criteria for chosing the elliptic function parameter m are discussed. Illustrative examples are presented with F being diverse polynomials of x.
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