At extreme cosmological distances, the property of mechanical equilibrium in surfaces lateral to the line of sight can be empirically tested; however, under the assumption of the cosmological principle, it cannot be detected parallel to the line of sight ( see timeline of the universe ).
32.
In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium.
33.
By linearly perturbing the equations defining the mechanical equilibrium of a star ( i . e . mass conservation and hydrostatic equilibrium ) and assuming that the perturbations are adiabatic, one can derive a system of four differential equations whose solutions give the frequency and structure of a star's modes of oscillation.
34.
In the planar case, the minimal number is 4, while in three dimensions one can build an object with just one stable and one unstable balance point, this is called slide at constant speed would be in mechanical equilibrium, but not in static equilibrium ( in the reference frame of the slide ).
35.
Two years later, Maupertuis cites Euler's 1744 work as a " beautiful application of my principle to the motion of the planets " and goes on to apply the principle of least action to the lever problem in mechanical equilibrium and to perfectly elastic and perfectly inelastic collisions ( see the 1746 publication below ).
36.
Supposing that the system were constantly at rest this meaning mechanical equilibrium ( i . e . net forces and torques zero ) with the two bodies thus hanging also at rest, but having " different " centrifugal forces upon them and consequently exerting different torques on the rod through the reactions of the tensions, the rod then would spontaneously rotate, in contradiction with our assumption that the system is at rest.
