In the context of a Lagrangian mechanics problem (a rigid pendulum of lenght l attached to a mass sliding w/o friction on the x axis), I found the following equations of motion and now I must solve them in the small oscillation limit. (I know the equations are correct)(adsbygoogle = window.adsbygoogle || []).push({});

[tex](m_1+m_2)\ddot{x}+m_2l\ddot{\theta}\cos(\theta)-m_2l\dot{\theta}^2\sin(\theta)=0[/tex]

[tex]l\ddot{\theta}+\ddot{x}\cos(\theta)+g\sin(\theta)=0[/tex]

I know that small thetas mean [itex]\cos\theta \approx 1[/itex] and [itex]\sin\theta\approx \theta[/itex] but why can we say that [itex]\dot{\theta}^2\approx 0[/itex]? The angle can be small and nevertheless vary furiously fast. What indicates that if theta is small, the so is its derivative?

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# Small angle approximation.

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