Typical examples of second order nonlinear dynamic systems

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Hi guys,
after hours of searching internet I couldn't find much real-life examples of second order nonlinear dynamic systems (only tons of tons of equation and system theory... got totally frustrated). They will serve as a base process for modeling controllers.
So far I found propeller pendulum and water tank / heating system.
I need some more ideas. Thanks
 

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flames and chemical reactions: first order derivative is the diffusion of the flame, second order is the convection and nonlinear exponential term is the reaction source (Arrhenius reaction).
[itex]\frac{d^2T}{dx^2}- \frac{dT}{dx}= A\cdot e^{C \cdot T}[/itex]

(edit: there is such an equation for all of the species in the reaction, and for the temperature, so these can be very large systems)
 

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