Abstract:  Temporal coupled-mode theory, playing an increasingly important role in frontier scientific research, is widely used in Mechanics, Optics, Electricity and other related disciplines. Under the concept of combining teaching and research in undergraduate, the introduction of temporal coupled-model theory into Theoretical Mechanics is a matter of urgency. In this paper, combine the Lagrangian equation and the secular perturbation theory, the second-order differential equation of oscillator coupling is degenerated to the first-order differential equation, that is, the main equation of temporal coupled-mode theory. The study provides a scheme for the smooth acceptance of temporal coupled-mode theory by undergraduate students and has implications in terms of undergraduate quality development.

Key words: temporal coupled-mode theory, Lagrangian equation, secular perturbation theory, teaching and research integration