| 词汇 | cotangent |
| 释义 | cotangent noun[ C ] mathematics specializeduk /kəʊˈtæn.dʒənt/ us /koʊˈtæn.dʒənt/ a function (= a mathematical relation) of an angle that is the reciprocal (= number) of tangent余切 Geometry: describing angles, lines & orientations angle of incidence angularity antinode asymptote asymptotic gradient multiaxial non-coplanar non-intersecting non-planar noncollinear reflex scalene triangle shallow sine supplementary triangulate unbowed vanishing point vertically cotangent | American Dictionarycotangent noun[ C ] us/koʊˈtæn·dʒənt/ trigonometry a function (= mathematical relation) of an angle that is the reciprocal (= number) of tangent Examples of cotangentcotangent Similarly, the second of equations (30) yields equation (32) and the inequality (33)with the tangent replaced by the minus cotangent. The cotangent bundle of a manifold is equipped with a canonical symplectic form and a canonical section (the vertical section). The metric g determines the isomorphism of the tangent and cotangent bundles. This condition is particularly significant, being verified in all natural mechanical systems on cotangent bundles. One of them is closely related to propagation of trajectories for symplectomorphisms of cotangent bundles. This transformation has an invariant form that comes from the symplectic form in the cotangent bundle of the billiard table. They may be geometrically interpreted as the forward propagation of tangents or the backward propagation of normals or cotangents. But why should forces take values in the cotangent bundle? This is more or less what is done when a tangent linear code is first developed and then the partials are used in the cotangent linear, or adjoint code. Typically, the cotangent space is defined as the dual space of the tangent space at "x", although there are more direct definitions (see below). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables (i.e. the cotangent space of configuration space). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Likewise, cotangent space is a contravariant functor, essentially the composition of the tangent space with the dual space above. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Important examples of vector bundles include the tangent bundle and cotangent bundle of a smooth manifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Abstractly, it is a second order operator on each exterior power of the cotangent bundle. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Readers familiar with more advanced mathematics such as cotangent bundles, exterior derivatives and symplectic manifolds should read the related symplectomorphism article. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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