Limiting phase trajectories and nonstationary resonance oscillations of the Duffing oscillator. Part 2. A dissipative oscillator

This paper extends the concept of limiting phase trajectories (LPT) to systems with dissipation. The Duffing oscillator with linear dissipation and periodic excitation is studied. Under condition of 1:1 resonance, we obtain an approximate analytic solution describing two stages of motion: at the first stage the trajectory is close to the non-dissipative LPT, while at the second stage the trajectory approaches stationary oscillations near the steady state.