I have an N-body system that I can simulate directly. For certain initial conditions, this system is unstable to a buckling behavior (exponential growth in an angle), and for others it's stable (oscillations). I've built a linearized model (Taylor series expansion) for the system of 2N coupled ODEs with numerically calculated coefficients. Using standard eigendecomposition methods I can get a spectrum of the modes for the linearized model.
However, I find that a system I know is stable when directly integrated has unstable linear modes within it. Could this make sense, or is it likely that I've made a mistake somewhere in the construction and calculate of my linearized ODE?