- Duffing oscillator
- Potential well escape (static/dynamic)
- Self-oscillation (limiting cycles)
- Bifurcations (various):
- changing phase diagram (Hopf)
- jumping between attractors (Lorenz)
- appearing/disappearing limiting cycle (VDP)
- stochastic
- Stochastic (sys. with 3 and more DOFs like stochastic pendulim, Lorenz attractor)
- Autoparametric resonance (modes coupling due to nonlinear terms)
- Sub/super-harmonic resonances (duffing)
- Instabilities (Mathieu equation, autoparametric resonances)
- Начать с Pi-теоремы размерности, которая превращает физическую задачу в чисто математическую
- показать, что в книге сказано про straightforward approach
- показать в Wikipedia нет зависимости от амплитуды
- Duffing (amplitude-frequency interaction, subharmonic resonance)
- Autoparametric resonance
- talk about nonlinear effects (self oscillations, limiting cycle, multivibrator)
- open original paper and show the generator and equations
- demonstrate notebook with derivation of limiting cycle for small amplitudes
- explain the difference
- show numerical examples
- open Nayfeh for demonstrating strong nonlinear case
- explain this derivation in my notebook
- show intersting thing in the original paper
W.L. Keith, R.H. Rand, Dynamics of a system exhibiting the global bifurcation of a limit cycle at infinity, International Journal of Non-Linear Mechanics, Volume 20, Issue 4, 1985, https://doi.org/10.1016/0020-7462(85)90040-X
- Nayfeh - Nonlinear oscillations
- Nayfeh - Perturbation methods
- Richard H. Rand - Lecture notes on nonlinear vibrations
- Strogatz - Nonlinear dynamics and chaos
- Tondl - Nonlinear vibrations
- Tondl - Autoparametric resonance in mechanical systems