Beat (acoustics)/Differential equations
Beat (acoustics) /Phase beats /Literature search /Just fifth displace stretch /Exact phase beats /Differential equations subpages drafts
| We need a review of coupled ordinary differential equations that contrasts the simplicity of linear ODEs with the complexity of nonlinear systems. |
Proposed style of this section edit
The article should be accessible to students with one year of calculus. On the linear equations, I would like to start with two coupled pendulums as shown in the figure. I think the would be best (with ) The students might not know what matrices are, so write them in non-matrix form and just show them the matrices with a link to matrices on wikipedia (or wikibooks or wikiversity.)
We need a figure showing the equivalent of the linearly coupled linear pendulums to horizontally oscillating masses on spring. That way we can use k and m in solving the problem (instead of g and l for a simple pendulum)
The van der pol oscillator will give them a hint as to the complexity of nonlinear systems.
Linear edit
Nonlinear edit
- w:Van der Pol oscillator
- International Journal of Non-Linear Mechanics, 29, pp. 737-753, 1994 Averaging Method for Strongly Nonlinear Oscillators with Periodic Excitations. R. Valéry Roy, R. Val'ery Roy link1 link2]
Tsatsos, Marios. "the Van der Pol equation." arXiv preprint arXiv:0803.1658 (2008)