The singularity of the anharmonic oscillator

[摘要] We have shown that a general solution to an anharmonic oscillation equation of a physical pendulum considered as a nonlinearity parameter function has a singularity at zero. This implies that applying different methods of regular decompositions in accordance with this parameter is impossible. We have developed a perturbation theory by using a new parameter of smallness in transformed canonical variables.

[发布机构] Samara State Aerospace University (SSAU), 34, Moskovskoye Shosse Street, Samara; 443086, Russia^1;148-32, Unyh Pionerov Prospect Street, Samara; 443105, Russia^2

[效力级别] 数学

[关键词] Anharmonic;Anharmonic oscillators;Canonical variables;General solutions;New parameters;Non-linearity parameter;Perturbation theory;Regular decomposition