Solution of Gylden-Lindstedt Equation
憲昭 渡辺, ノリアキ ワタナベ, Noriaki Watanabe · Institutional Repositories DataBase (IRDB) · 2007
It often occurs in the celestial mechanics a linear differential equation with a periodic coefficient d^2x/dt^2+m^2x=2εxcosw',w'=λt+β, where m, λ, β are given constants and ε is a small given constant. In the present paper I give a solution and its mean motion of the above equation up to the 6th order of ε by making use of Lindtstedt's method which does not give rise to mixed secular terms.