Cov txheej txheem:

Dab tsi yog arc length parameterization?
Dab tsi yog arc length parameterization?

Video: Dab tsi yog arc length parameterization?

Video: Dab tsi yog arc length parameterization?
Video: Vector Calculus | Length of Curve with Example Solved | Mathematics 2 New Syllabus | Maths 2 GTU 2024, Kaum ib hlis
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Yog hais tias lub particle mus ntawm qhov tsis tu ncua ntawm ib chav tsev ib ob, ces peb hais tias qhov nkhaus yog parameterized los ntawm arc ntev . Peb tau pom lub tswv yim no ua ntej hauv lub ntsiab lus ntawm radians. Nyob rau hauv ib lub voj voog ib lub radian yog ib chav tsev ntawm arc ntev ncig lub voj voog.

Tib neeg kuj nug, ua li cas koj xam qhov ntev arc?

Yog tias lub kaum sab xis ntawm koj lub arc ntsuas hauv degrees ces siv cov qauv no los xam qhov ntev ntawm arc:

  1. luas arc (A) = (Θ ÷ 360) x (2 x π x r)
  2. Luas A = (Θ ÷ 360) x (D x π)
  3. A = Arc length.
  4. Θ = Lub kaum sab xis (hauv degrees)
  5. r = lub voj voog ntawm lub voj voog.
  6. A = r x Θ
  7. A = length of arc.
  8. r = lub voj voog ntawm lub voj voog.

Ib yam li ntawd, nws txhais li cas rau parameterize ib nkhaus? Hauv kev ua lej, thiab tshwj xeeb tshaj yog hauv geometry, parameterization (los yog parameterization ; kuj parameterisation, parametrisation) yog tus txheej txheem ntawm kev nrhiav parametric sib npaug ntawm a nkhaus , ib tug nto, los yog, feem ntau, ib tug manifold los yog ntau yam, txhais los ntawm ib tug implicit equation.

Tib neeg kuj nug, qhov curvature ntawm nkhaus yog dab tsi?

Intuitively, cov curvature yog tus nqi uas a nkhaus deviates los ntawm txoj kab ncaj nraim, los yog ib qho deviates los ntawm kev ua dav hlau. Rau nkhaus , tus piv txwv canonical yog lub voj voog, uas muaj a curvature sib npaug rau qhov sib npaug ntawm nws lub vojvoog. Cov voj voog me me khoov ntau dua, thiab yog li muaj siab dua curvature.

Koj ua li cas parameterize ib kab segment?

Nrhiav ib parameterization rau cov kab ntu nruab nrab ntawm cov ntsiab lus (3, 1, 2) thiab (1, 0, 5). Kev daws: Tsuas yog qhov sib txawv ntawm qhov piv txwv 1 yog tias peb yuav tsum txwv qhov ntau ntawm t kom tus kab ntu pib thiab xaus ntawm cov ntsiab lus muab. Peb ua tau parameterize tus kab ntu x = (1, 0, 5) + t(2, 1, −3) for0≦t≦1.

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