## Testing LaTeX

*February 16, 2019*

Trying out a bit more of the features, for example the LaTeX environment with the Euler-Lagrange equations for a one-dimensional system:

$$\delta S=\delta\int*{t*1}^{{t_2}} L dt =0 \quad \Rightarrow \quad \frac{d}{dt}\frac{\partial L}{\partial \dot{q}}-\frac{\partial L}{\partial q}=0 $$

Update: Well, that does not look that nice -_-. Will have to remember trying that again some time later. Maybe I find some workaround.

What it would have been:

The right side states the Hamilton principle of stationary action - a system evolves in such a way, that small changes to its state have no effect on its trajectory (or at least an infinitesimally small one).

From this principle follow the equations of motion of the system as shown on the right side. Those are now "just" simple partial differential equation, which can be solved - sometimes analytically, more often just numerically.

Of course this does not answer the question how to formalize a system and what those equations then tell us about the development of the system. But it is nice to have at least a middle part that is comparatively straight forward.