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The meter can exchange energy with the environment (e.g. it can absorb heat), so energy of the meter is not conserved. Yet, the meter as a solid object is stable. If the meter was made from liquid it would not be stable (and not useful as a meter) even when it's energy is constant. This demonstrates that stability and energy conservation are not directly related to each other.RockyMarciano said:how do you maintain this stability without conservation laws in a dynamical context?
More formally, consider a particle in a potential of the form
$$V(x,t)=\frac{kx^2}{2}+U(t)$$
where ##U(t)## is a positive non-constant function of time ##t##. Clearly this potential does not conserve energy. Yet, the particle position ##x=0## is stable, provided that ##k## is positive. If ##k## were negative the position ##x=0## would not be stable, even if ##U(t)## were zero. That's another demonstration that stability and energy conservation are not related.
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