rigidità

Rigidity denotes the resistance of an object or structure to deformation when subjected to external forces. The term is used across disciplines with different emphases: in mechanics and materials science it relates to stiffness; in geometry and topology it concerns whether a configuration is uniquely determined by a limited set of constraints; in biology and chemistry it can describe how easily a system can move or rearrange.

In physics and engineering, a rigid body is an idealization whose shape does not change under motion. Real objects deform slightly, but the rigid-body approximation simplifies dynamics. The stiffness of materials is quantified by elastic moduli such as Young’s modulus and the shear modulus; higher moduli indicate greater resistance to stretching or shearing. Structural rigidity arises when joints and members constrain deformation, enabling predictable behavior under loads.

In mathematics, rigidity refers to properties where a structure is determined by minimal or local data. Examples include geometric rigidity results, such as Cauchy’s rigidity for convex polyhedra, and Mostow’s rigidity for certain hyperbolic manifolds. Rigidity theory also studies frameworks of bars and joints to determine when a configuration is unique up to congruence, often using rigidity matrices and combinatorial conditions.

In biology and materials science, rigidity can describe cellular or molecular stiffness, such as muscle rigidity in medicine, where there is increased resistance to passive movement, seen in conditions like Parkinson’s disease. In chemistry and polymer science, network cross-linking or molecular constraints can increase rigidity, reducing conformational freedom and affecting properties like elasticity and phase behavior.