Manifolds - Revision history

Admin at 02:45, 16 March 2013

2013-03-16T02:45:05Z

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	* READ THIS FIRST		A hydraulic '''manifold''' is a manifold that regulates fluid flow between [[pumps]] and [[actuators]] and other components in a hydraulic system. It is like a switchboard in an electrical circuit because it lets the operator control how much fluid flows between which components of a hydraulic machinery. For example, in a backhoe loader a manifold turns on or shuts off or diverts flow to the telescopic arms of the front bucket and the back bucket. The manifold is connected to the levers in the operator's cabin which the operator uses to achieve the desired manifold behaviour.
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	[[~~File:Manifold.gif\|thumb\|right\|Manifolds~~]]		A manifold is composed of assorted hydraulic valves connected to each other. It is the various combinations of states of these [[valves]] that allow complex control behaviour in a manifold.

	In mathematics, a '''Manifold''' of dimension n is a topological space that near each point resembles n-dimensional Euclidean space. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. Lines and circles, but not figure eights, are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and thetorus, which can all be realized in three dimensions, but also the Klein bottle and real projective plane which cannot.

	The surface of the earth requires two charts to include every point. Although near each point, a manifold resembles Euclidean space, globally a manifold might not. For example, the surface of the sphere is not a Euclidean space, but in a region it can be charted by means of geographic maps: map projections of the region into the Euclidean plane. When a region appears in two neighbouring maps , the two representations do not coincide exactly and a transformation is needed to pass from one to the other, called a transition map.
	The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be described and understood in terms of the relatively well-understood properties of Euclidean space. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. Manifolds may have additional features. One important class of manifolds is the class of differentiable manifolds. This differentiable structure allows calculus to be done on manifolds. A Riemannian metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model spacetime in general relativity.

	==Sources==		==Sources==
			[http://en.wikipedia.org/wiki/Hydraulic_manifold Wikipedia Manifold]
	[http://en.wikipedia.org/wiki/~~Manifold~~ Wikipedia Manifold]

Kodiyath at 05:41, 9 December 2012

2012-12-09T05:41:16Z

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