On the stability of the motion of a Birkhoffian system (Q1338054)

First, we give the first approximation equations for Birkhoffian systems. Secondly, we discuss the properties of the characteristic equation of the first approximation equations with constant coefficients and show that the eigenvalues of the characteristic equation always appear in pairs. Using Lyapunov's theorem of stability in the first approximation, we obtain that the Birkhoffian system is unstable or critical.