 MechanicsSaunders Mac Lane
Chapter Chapter IX in Mathematics Form and Function, 1986, pp 259-306 from Springer Abstract: Abstract There is a remarkable interaction between theoretical constructions in Science and conceptual notions in Mathematics: the same idea—or the same idea, disguised, may arise both in Science and in Mathematics. This interaction is especially visible in the relations between theoretical Physics and pure Mathematics, where it first became apparent in mechanics at the hands of Galileo and in the invention of the calculus by Newton. One may say that the calculus (which dominated the development of Mathematics for at least two centuries) was developed by Newton in order to tackle problems of mechanics, especially those of celestial mechanics. This is only one of the striking interactions we have in mind. Today there is a amazing confluence of the gauge theories in Physics (for the Yang-Mills equations) and the geometrical theory of connections on fiber bundles. It is the aim of this chapter to sketch some of these developments. Though we cover only a small number of items, they are intended as samples of many decisive interactions between Science and Mathematics. Keywords: Tangent Bundle; Configuration Space; Lagrange Equation; Order Differential Equation; Legendre Transformation (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-4872-9_10 Ordering information: This item can be ordered from DOI: 10.1007/978-1-4612-4872-9_10 Access Statistics for this chapter More chapters in Springer Books from Springer |
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