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The ancient Greeks applied analysis only to static problems either to pure geometry or to forces in equilibrium.
With its forces in equilibrium, the truss exerts only a direct downward pressure on the walls, so that they need not be thickened or buttressed.
An atomic force microscope (AFM) is a very powerful tool to evaluate interaction forces between surfaces in liquids on the molecular scale, but the apparatus was not designed to measure forces in equilibrium.
We address the Thrust Network Analysis (TNA), i.e. the methodology for modeling masonry vaults as a discrete network of forces in equilibrium with gravitational loads, first contributed by O'Dwyer and fully developed by Block and coworkers.
The resulting mathematical eigenvalues and eigenvectors, respectively indicative of natural frequencies and modes of oscillation, are then assumed to be continuous functions of a scalar factor upon a normalised set of forces in equilibrium.
To determine ionospheric currents, we start with a simplified momentum equation assuming steady state conditions and all forces in equilibrium.
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When the simulation is running, the particles try to reach a distance where these forces are in equilibrium, this distance can be presented as r = k e q 1 q 2 − k s k 3. The global damping constant representing friction is subtracted from the forces using the following formula F = - kv, where - k is the global damping constant and v is the velocity.
The theory observes that bending-strain gradients are invariable under constant internal force held in equilibrium by the transverse shear stresses in the corrugated cross-section.
The tilde in K ∼ T serves the purpose of distinguishing the tangent stiffness matrix from tensor functions K T which refer to internal forces that are not in equilibrium with the external forces [1].
In level flight, a bird must flap its wings to generate lift, and an optimum wing-flapping frequency exists at which lift and gravity forces on the bird are in equilibrium and mechanical power is minimum for sustainable flight performance [11].
This was the first example where the p Ka change of the indicator was suggested as the driving force for a change in equilibrium conditions of an ion-sensing membrane.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com