The twist coefficient of periodic solutions of a time-dependent Newton's equation
A \(T\)-periodic solution \(\varphi\) of a \(T\)-periodic equation \(x''+f(t,x)=0\) is considered. It is supposed that \(\varphi\) is generic non zero twist type up to the 4th order terms. If \(f(t,x)=a(t)x+b(t)x^ 2+c(t)x^ 3+\dots\) and \(\varphi(t)\equiv 0\) then conditions for the coefficients (boundedness and sign type) are formulated, which guarantee that the trivial solution is of twist type and as a consequence Lyapunov stable. The results are illustrated by examples including the pendulum of variable length.
scientific article; zbMATH DE number 96102
scientific article