Gauss the principle

for toporo the "coercion" Z is at each moment of time smallest. It is established K. By Gauss (1829).

Physical value, NAZ. by "coercion", it is introduced as follows. Free material point with a mass of t under the effect on it of the assigned force of F will have an acceleration F/mzh but if to the point they are superimposed connection, then its acceleration under the effect of the same force of F will become equal some to other value w. Then the deviation of point from the free motion, caused by the action of connection, will depend on a difference in these accelerations, i.e. from value Z, proportional to the square of this difference, and NAZ. by "coercion". For one point

and for the mech. system Z it is equal to the sum of such values.

Let us examine, for example, the point, which begins to move along the smooth inclined plane from the position A without the initial velocity (see fig.). For it kinematically any possible displacement AV, AB₁, AV₂... in this plane with some accelerations of w, w₁, w₂...; however, with the free drop point would complete displacement Afrom lengthwise the vertical line with an acceleration of g. Then the deviations of point from the free motion are depicted as sections SV, SV₁, SV₂..., smallest of which the section SV, perpendicular to the inclined plane, will be. Consequently, "coercion" Z, proportional to squares SV, SV, SV₂..., will be smallest during the motion along the line of the smallest slope AD. This there will be the proper motion of point, proceeding with the acceleration

G. p. use for the composition of the equ. of the motion of mech. systems and study of the properties of these motions.

It is cast. see with st. Variation principles of mechanics.