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- from D.M. Klimov, V.M. Rudenko, Computer Algebra Methods in
Mechanics, Nauka, (1989).
- nonlinear periodic movement, nonlinear ordinary differential equation

- new time variable
,
is an unknown frequency

- Poincare perturbation method--expansion into a power series

- example: the van der Pol equation

- after substituting power series in

- initial condition
- zeroth order solution
- first order solution

- after Fourier expansion

- no secular terms in the solution require zero coefficients of
and
on the right hand side

- solution

- using the initial condition
- second order equation

- first order solution

- second order solution

- etc. for higher orders
Richard Liska