For any complex model, an equivalent model of a complex system can be found by using piecewise time-invariant linear system models derived along disturbed trajectories resulting from simulation studies. The method of trajectory section eigenvalues has the same assumptions used for numerical integration, namely that the system is time-invariant linearized in and only in a single simulation step. Therefore, in each integration step, not only the energy margin of the trajectory section can be analyzed by using a static extended equal-area criterion (EEAC) method, but also the oscillation damping and instantaneous frequency of the trajectories section can be observed with the analysis of equilibrium point eigenvalues, regarding the unbalanced power and kinetic energy in the section as the initial disturbance. The complete disturbed trajectory forms a uniform basis for large and small disturbance stability analysis. Section eigenvalues can reflect the effect of complex factors of the oscillation characteristics, and EEAC can reflect the essence of the complicated influence on synchronous stability. Introducing the concept of "sequences of trajectory section eigenvalues at the virtual equilibrium point", the influence of section kinetic energy on the pole-slip instability can be taken into account, in association with the two mechanisms of pole-slip instability and oscillatory instability. The oscillation damping and instantaneous frequency of far end point (FEP) and dynamic saddle point (DSP) are analyzed and the essential relations of large disturbance instability and small disturbance instability are revealed.