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Rigidity is the property of a structure that it does not bend or flex under an applied force. The opposite of rigidity is flexibility.In structural rigidity theory, structures are formed by collections of objects that are themselves rigid bodies, often assumed to take simple geometric forms such as straight rods (line segments), with pairs of objects connected by flexible hinges.
Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges; Rigidity (electromagnetism), the resistance of a charged particle to deflection by a magnetic field; Rigidity (mathematics), a property of a collection of mathematical objects (for instance sets or functions)
Shear strain. In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: [1]
Axial parallelism (also called gyroscopic stiffness, inertia or rigidity, or "rigidity in space") is the characteristic of a rotating body in which the direction of the axis of rotation remains fixed as the object moves through space. In astronomy, this characteristic is found in astronomical bodies in orbit.
In particle physics, rigidity is a measure of the resistance of a particle to deflection by magnetic fields, defined as the particle's momentum divided by its charge. For a fully ionised nucleus moving at relativistic speed , this is equivalent to the energy per atomic number.
Rigidity in space describes the principle that a gyroscope remains in the fixed position on the plane in which it is spinning, unaffected by the Earth's rotation. For example, a bike wheel. Early forms of gyroscope (not then known by the name) were used to demonstrate the principle.
The rotating disc and its connection with rigidity was also an important thought experiment for Albert Einstein in developing general relativity. [4] He referred to it in several publications in 1912, 1916, 1917, 1922 and drew the insight from it, that the geometry of the disc becomes non-Euclidean for a co-rotating observer. Einstein wrote ...
The first result demonstrates when rigidity and infinitesimal rigidity of tensegrities are equivalent. Theorem. [ 20 ] Let ( G , p ) {\displaystyle (G,p)} be a d {\displaystyle d} -dimensional tensegrity framework where: the vertices of G {\displaystyle G} are realized as a strictly convex polygon; the bars form a Hamilton cycle on the boundary ...