Structural rigidity

In discrete geometry and mechanics, structural rigidity is a combinatorial theory for predicting the flexibility of ensembles formed by rigid bodies connected by flexible linkages or hinges.

Definitions

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. A structure is rigid if it cannot flex; that is, if there is no continuous motion of the structure that preserves the shape of its rigid components and the pattern of their connections at the hinges.

There are two essentially different kinds of rigidity. Finite or macroscopic rigidity means that the structure will not flex, fold, or bend by a positive amount. Infinitesimal rigidity means that the structure will not flex by even an amount that is too small to be detected even in theory. (Technically, that means certain differential equations have no nonzero solutions.) The importance of finite rigidity is obvious, but infinitesimal rigidity is also crucial because infinitesimal flexibility in theory corresponds to real-world minuscule flexing, and consequent deterioration of the structure.

Step

Step or Steps may refer to:

List of Rock Profile episodes

Here is a list of episodes in Matt Lucas and David Walliams' comedy show Rock Profile. Also see Rock the Blind.

Series One (1999–2000)

Series Two (2000 - 2001)

Series Three (2009)

Steps (group)

Steps were a British dance-pop group consisting of Claire Richards, Faye Tozer, Lisa Scott-Lee, Ian "H" Watkins and Lee Latchford-Evans. Steps formed in May 1997 and released four studio albums, three compilation albums and seventeen singles. Their music has a 1990s dance-pop, house, electropop and bubblegum dance sound. Their name was based on a marketing premise: that each of their music videos were to be choreographed, and the dance steps were included in the sleeve with most of their singles.

Steps achieved a series of charting singles between 1997 and 2001 including two number-one singles in the UK (one a double A-side), two number-one albums in the UK, 14 consecutive top 5 singles in the UK and a string of hits throughout Europe. The group has sold over 20 million records worldwide in addition to acquiring a BRIT Award nomination in 1999 for Best Newcomer while supporting Britney Spears on tour the same year. When Richards and Watkins departed, the group disbanded on 26 December 2001. Their penultimate single reached number five in the UK charts while their final album of greatest hits, Gold (2001), was the group's second number-one album in the UK.