Summary: Small oscillations of an undamped holonomic mechanical system with varying parameters are described by the equations
A nontrivial solution is called small if
It is known that in the scalar case , , there exists a small solution if is increasing and tends to infinity as .
Here we give sufficient conditions for the existence of a small solution of the general system in the case when coefficients , are step functions. The method of proof is based on a transformation reducing the ODE to a discrete dynamical system. The results are illustrated by examples of coupled harmonic oscillator and double pendulum.