Least Curvature, Principle of

Least Curvature, Principle of

 

one of the variational principles of mechanics. It establishes that in the absence of active (given) forces, of all kinematically possible trajectories (that is, those permitted by constraints), the true trajectory will be the one that has the least curvature. This principle is also called the principle of the most direct path, and it can be viewed as a generalization of the law of inertia.

The principle of least curvature is closely associated with the Gauss principle of least constraint, since the quantity called constraint is proportional to the square of the curvature; with ideal constraints, both principles have identical mathematical expression. The principle of least curvature was applied by Heinrich Hertz in constructing his mechanics, in which the effect of active forces changes with the introduction of the corresponding constraints.

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