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Are there any "linear" lagrangian systems of interest for which an analytic solution is not obvious?
Out of curiosity, I am interested in Lagrangian dynamical systems that can be expressed in a "linear" manner. By this, I mean that their Lagrangian can be expressed, quadratically, as
$$L = \...
- 175
2
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3
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How to justify this small angle approximation $\dot{\theta}^2=0$?
Suppose the equation of motion for some oscillating system takes the following form:
$$\ddot{\theta}+\dot{\theta}^2\sin\theta+k^2\theta\cos\theta=0$$
Applying small angle approximation to $\theta$ ...
- 205
2
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Linearized equations
What is $V_{\alpha\beta}$?
And what is a symmetric, positive definite potential energy matrix?
And why is there a linearized equation like this?
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