Undergrad "A system tries to minimize total potential energy"

[Swamp Thing]

While reading this thread on Stack Exchange... https://physics.stackexchange.com/q...oes-a-system-try-to-minimize-potential-energy ... a question came to mind : -

Say an object is launched away from Earth at a velocity greater than the escape velocity. This system will not end up with its potential energy less than the initial value. Apparently, therefore, we need to qualify the principle of "tendency towards minimum potential energy" so as to exclude such cases? If so, how would we do that rigorously?

 

[Dale]

As far as I know it only applies to bound systems that can irreversibly exchange energy with another system

 

[vanhees71]

There's energy conservation for a closed system. Usually the kinetic and potential energy both change with time but such that the total energy stays constant. Take the harmonic oscillator as an example:
$$m \ddot{x}=-D x.$$
The general solution is
$$x(t)=x_0 \cos(\omega t -\varphi_0),$$
where the amplitude, $x_0$, and "phase", $\varphi_0$ are integration constants, and $\omega=\sqrt{D/m}$.

The kinetic and potential energies are
$$T=\frac{m}{2} \dot{x}^2, \quad V=\frac{D}{2} x^2.$$
As a function of time you get
$$T=\frac{m \omega^2}{2} \sin^2(\omega t -\varphi_0), \quad V=\frac{D}{2} x_0^2 \cos^2(\omega t-\varphi_0).$$
Now $m \omega^2=D$ and thus the total energy
$$E=T+V=\frac{D}{2} x_0^2 [\sin^2(\omega t-\varphi_0) + \cos^2(\omega t-\varphi_0)]=\frac{D}{2} x_0^2=\text{const}.$$

 

[Vanadium 50]

You're anthropomorphizing inanimate systems. They hate it when you do that.

If you have a system with two energy reservoirs, of any kind (potential and kinetic is but one example), and all the energy is in one, the only thing the system can do with the energy is move it to the other. There is nothing more to this than "if you're all the way to the left, the only direction you can move is to the right".

While reading this thread on Stack Exchange..

Is that's confusing you, maybe you should go elsewhere.