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A procedure to obtain the initial amplitude and phase for the Krylov–Bogoliubov method

✍ Scribed by R.A. Rink

Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
401 KB
Volume
303
Category
Article
ISSN
0016-0032

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✦ Synopsis

Using the Krylov-Bogoliubov method for obtaining analytical solutions to systems with small non-linearities, a procedure is employed to determine the initial amplitude and phase in terms of the initial displacement and velocity. Equations representing the time rate of change of amplitude and phase are used directly. Whether the corresponding linear equations of the non-linear system has purely imaginary, complex conjugate or real roots, the same procedure can be applied.

An example is given which demonstrates the initial amplitude and phase change for various higher order approximations.

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