Carl Friederick Gauss in 1829 established this principle for Classical Mechanics.
"According to the Gauss principle,"the motion of a system of material points, constrained in an arbitrary manner, and subjected to arbitrary forces at any moment of time, takes place in a manner which is as similar as possible to the motion that would be performed by these points if they were free, i.e. with least-possible forcing — the measure of forcing during the time dt being defined as the sum of the products of the mass of each point and the square of the distance of the point from the position which it would occupy if it were free" "
You can read a little more here.
"According to the Gauss principle,"the motion of a system of material points, constrained in an arbitrary manner, and subjected to arbitrary forces at any moment of time, takes place in a manner which is as similar as possible to the motion that would be performed by these points if they were free, i.e. with least-possible forcing — the measure of forcing during the time dt being defined as the sum of the products of the mass of each point and the square of the distance of the point from the position which it would occupy if it were free" "
You can read a little more here.
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