- 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