Statics

A branch of mechanics in which the equilibrium of material bodies under the influence of forces and the equivalency conditions of force systems are studied. The equilibrium is studied with respect to a system of reference in which all forces that affect the material bodies are defined (for example, equilibrium with respect to the Earth). As in dynamics, models of real bodies are used in statics which enable one to reduce the problem of equilibrium to simpler problems. These models include a material point, an elastically-deformable body, a rigid body, a continuum, an ideal liquid, a viscous liquid, etc. Depending on the properties of the material bodies, statics is understood to mean the statics of a rigid body, the statics of an elastically-deformable body, the statics of a liquid, and the statics of a gas. Research into statics splits into geometrical and analytical methods.

Geometrical statics studies the geometrical properties of force systems (force vectors) that affect the system of material points under consideration, the construction of equivalent force systems, the reduction to their simplest form, and the establishment of conditions of equilibrium of force systems and the bodies affected by these forces. The most important topic in geometrical statics is the statics of a rigid body.

Analytical statics is based on the concept of the work done by forces acting on the system of material points under an arbitrary possible displacement of the system. The basic principle of analytical statics is the principle of virtual displacements (cf. Virtual displacements, principle of).

The study of statics dates back to Ancient times, and its beginnings are attributed to the Greek mathematician Archimedes. The basic laws of the equilibrium of geometric statics were established by the Dutch mechanician S. Stevin and the French mechanician and geometer L. Poinsot. The first general formulation of the principle of virtual displacements is attributed to J. Bernoulli. J.L. Lagrange was the first to prove the principle of virtual displacements and to obtain results on the equilibrium of a system.

References

[1]	L. Poinsot, "The foundations of statics" , Moscow (1920) (In Russian; translated from French)
[2]	J. Bernoulli, "Selected essays on mechanics" , Moscow (1937) (In Russian; translated from French)
[3]	J.L. Lagrange, "Mécanique analytique" , 1 , Blanchard, reprint , Paris (1965) ((Also: Oeuvres, Vol. 11.))
[4]	M.V. Ostrogradskii, "General considerations on the moments of forces" , Selected works , Moscow (1958) (In Russian)
[5]	N.E. Zhukovskii, "Theoretical mechanics" , Moscow-Leningrad (1952) (In Russian)
[6]	S.A. Chaplygin, "Courses of lectures on theoretical mechanics" , Collected works , 4 , Moscow-Leningrad (1949) (In Russian)
[7]	P. Appell, "Traité de mécanique rationelle" , 1 , Gauthier-Villars (1953)

References

[a1]	R. Marcolongo, "Theoretische Mechanik" , I , Teubner (1911)
[a2]	R.B. Lindsay, H. Margenau, "Foundations of physics" , Dover, reprint (1957)