Lindstedt Duffing Secular Removal
Remove a growing perturbation term by correcting an oscillator’s frequency.
Free theory articleRemove a growing perturbation term by correcting an oscillator’s frequency.
Concept & interpretation
Weak hardening oscillators governed by the equation y'' + y + εy3 = 0 exhibit secular growth when solved using a naive first-order perturbation approach. The Lindstedt-Poincaré method introduces a strained time variable, τ = ωt, correcting the frequency to eliminate the unbounded term and capture bounded periodic motion asymptotically.
Interactive Experiment
Open the Lindstedt Duffing Secular Removal module.
- Set the Nonlinearity epsilon to 0.1, Amplitude to 1, and Time to 20.
- Observe the Secular correction value. It grows linearly in magnitude, causing the Naive perturbation to diverge from bounded periodic motion.
- Check the Strained-time perturbation value, which remains bounded across large time intervals.
- Increase Time to 40. The Secular correction term grows even larger, highlighting the breakdown of the naive solution, while the Strained solution stays bounded within the expected amplitude range.