Two rigid bodies are said to be equal (copies of each other) if there is a mathematical proper rotation, that applied to one, gives the same physical state as the other, or correspondingly, if removal of one object and a combination of rotations of the other to the position of the first is possible, provided that no other objects are in the way, and locally creates the same physical situation as before. Thus they have the same shape and size, a corresponding density distribution, etc. Jump to: navigation, search In physics, a rigid body is an idealisation of a solid body of finite size in which deformation is neglected. ... In geometry, an improper rotation is the combination of an ordinary rotation of three-dimensional Euclidean space, that keeps the origin fixed, with a coordinate inversion (a vector x goes to −x). ... Rotation is the movement of a body in such a way that the distance between a certain fixed point and any given point of that body remains constant. ... In geometry, two objects are of the same shape if one can be transformed to another (ignoring color) by dilating (that is, by multiplying all distances by the same factor) and then, if necessary, rotating and translating. ... In general English usage, length (symbols: l, L) is but one particular instance of distance – an objects length is how long the object is – but in the physical sciences and engineering, the word length is in some contexts used synonymously with distance. Height is vertical distance; width (or breadth...

This definition can be extended to elastic bodies (where the shapes depend on the forces on the bodies). In that case we can use the second definition, or, if using the first, compare situations where the forces are also rotated. There are separate articles about elasticity in economics, and about British rubber bands. ...

If a composite object allows some reversible internal movement, such as in the case that it has a hinge, or in the case of a chain, two of them are still equal if also this internal movement has to be applied to make them correspond. Similarly, two objects may still be considered the same even if one has a higher temperature with corresponding thermal expansion, etc. A reversible process (or reversible cycle if the process is cyclic) , in thermodynamics, is a process that can be reversed by means of infinitesimal changes in some property of the system (Sears and Salinger, 1986). ... A hinge is a mechanical device that connects two solid objects, allowing rotation between them. ... Look up Chain on Wiktionary, the free dictionary A chain can be any of the following: a flexible connection through multiple rigid links; applications include: pulling (it cannot be used for pushing) power transmission, as in roller chains (e. ... Jump to: navigation, search In physics, thermal expansion is the tendency of matter to increase in volume or pressure when heated. ...

In a stricter sense, "the same object" can mean the same example, not a copy. In that case other conditions, such as reversibility, may be relaxed. See also identity. // Computer programming In object-oriented programming, object identity is a mechanism for distinguishing different objects from each other. ...