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curvilinear coordinates是什麼意思,curvilinear coordinates的意思翻譯、用法、同義詞、例句

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  • 曲線坐标

  • 例句

  • In this paper the cosine transform matrix relating Cartesian coordinates with orthogonal curvilinear coordinates is introduced.

    本文介紹笛卡爾坐标與正交曲線坐标的"餘弦變換矩陣",證明這個變換矩陣是正交矩陣。

  • Based on the fact, regarding the pipe of direct-buried pipe as cylindrical shell , the article establishes curvilinear coordinates, and analyzes the loading on the pipe.

    根據工程實際,利用彈性薄殼理論,将直埋管道直管段作為柱殼建立物理模型,并在相應曲線坐标下,對作用于管道上的荷載進行受力分析。

  • In curvilinear coordinates, a numerical simulation model for wave propagation on non-uniform current in water of slowly varying topography was presented with employing self-adaptive grids method.

    利用自適應網格技術,建立了曲線坐标系下緩變水深水域非均勻水流中波浪傳播的數值模拟模型。

  • A new idea is suggested to extend the viscous vector equations in non-orthogonal curvilinear coordinates.

    本文讨論在非正交曲線坐标系中,粘性流矢量方程一種新的展開思路。

  • Orthogonal Curvilinear Coordinates. Questions on Homework 2.

    正交曲線座标。讨論作業2。

  • In calculation of inner flew field within turbomachinery, partial differentials of three unit vectors in a curvilinear orthogonal coordinates must be employed.

    在葉片式流體機械的内流場計算中,要使用曲線坐标系的三個正交單位矢量關于曲線坐标的偏導數。

  • The govern equations, the separation and numerical solution of the govern equation in the orthogonal curvilinear coordinates, the boundary condition and the movable boundary technique were given.

    給出了正交曲線坐标系下二維動床數學模型的控制方程、控制方程的高散及數值解法、邊界條件及動邊界技術。

  • Precise expression of element stiffness matrices and equivalent nodal load vector are derived in curvilinear coordinates based on variational principle.

    利用變分原理在曲線坐标系下推導了單元剛度矩陣的顯式及其等效結點荷載列陣。

  • By matrices and a derivative formula, a ****** method of deriving accelerations in orthogonal curvilinear coordinates based on variable transformation is proposed.

    利用矩陣和一個微商公式,把變量替換法求正交曲線坐标系中加速度運算的繁瑣程度大為降低。

  • Two-phase turbulent reacting flow model of the internal operating processes in Liquid Rocket Engine (LRE) is set up in non-orthogonal curvilinear coordinates.

    建立了任意斜交曲線坐标系下液體火箭發動機(LRE)内部工作過程的氣液兩相湍流化學反應流模型。

  • Using the cosine transform matrix the Cartesian tensors, differential operators and related equations can be readily transformed into corresponding expressions in orthogonal curvilinear coordinates.

    利用這個變換矩陣可以方便地将笛卡爾坐标的張量表達式、微分算子及有關公式變換成正交曲線坐标的相應公式。

  • This paper is concerned with a turbulence mathematical model under orthogonal curvilinear coordinates including the effects of streamline curvature on turbulent flow.

    考慮彎曲邊界曲率效應對水流水力特性的影響,建立了正交曲線坐标系下的紊流數學模型。

  • The model system is in the generalized curvilinear coordinates, using high precision self-adaptive grids to fit the complicated topographies and coastal shapes.

    模型系統采用廣義曲線坐标系下的形式,使用高精度的自適應網格拟合複雜岸界。

  • ADI method is used to solve the transformed equations under orthogonal curvilinear coordinates, and the polluted matter diffusion term is considered.

    采用ADI法求解正交曲線坐标系下水流及污染物濃度輸移的耦合方程時,計及了水流擴散項的影響。

  • In this paper, a numerical calculation is presented for orthogonal and non-orthogonal curvilinear coordinates in a cascade of turbomavhinery.

    本文讨論了葉栅中正交與非正交曲線坐标系的數值求解方法。

  • In this paper the cosine transform matrix relating Cartesian coordinates with orthogonal curvilinear coordinates is introduced. It is shown that this transform matrix is an orthogonal matrix.

    本文介紹笛卡爾坐标與正交曲線坐标的"餘弦變換矩陣",證明這個變換矩陣是正交矩陣。

  • By defining generalized velocities and generalized accelerations, velocities and accelerations in orthogonal curvilinear coordinates are obtained.

    利用矩陣和一個微商公式,把變量替換法求正交曲線坐标系中加速度運算的繁瑣程度大為降低。

  • 專業解析

    曲線坐标系(curvilinear coordinates)是數學和物理學中用于描述空間幾何結構的一種坐标系統,其坐标線可以是任意曲線而非僅限于直線。與笛卡爾坐标系的網格線為直線不同,曲線坐标通過非線性變換定義,適用于對稱性較強或邊界複雜的物理問題。

    定義與數學基礎

    曲線坐标通過參數化的曲面或曲線定義,例如極坐标系(( r, theta ))、柱坐标系(( rho, phi, z ))和球坐标系(( r, theta, phi ))。其核心數學工具包括:

    1. 拉梅系數(Lame coefficients):用于描述坐标軸的縮放因子。例如,球坐标系中的線元表達式為: $$ ds = dr + r dtheta + r sintheta , dphi, $$ 對應拉梅系數 ( h_r=1 ), ( h_theta=r ), ( h_phi=rsintheta )。
    2. 協變與逆變基向量:通過偏導數定義局部基向量,滿足正交性或非正交性條件。

    應用領域

    1. 物理學:廣義相對論中,愛因斯坦場方程在曲線坐标系下描述時空彎曲;電磁學中,柱坐标系簡化了無限長帶電導體的場計算(參考《經典電動力學》J.D. Jackson)。
    2. 工程學:流體力學模拟圓柱繞流時,極坐标系減少計算複雜度(MIT開放課程案例)。
    3. 計算機圖形學:參數化曲面(如貝塞爾曲面)依賴曲線坐标實現三維建模。

    權威參考資料

    網絡擴展資料

    Curvilinear coordinates(曲線坐标系) 是幾何和數學分析中用于描述空間的一種坐标系,其特點是坐标線可能為曲線而非直線。以下是詳細解釋:

    1.基本定義

    2.與笛卡爾坐标系的區别

    3.數學特性

    4.應用領域

    5.示例

    總結來說,曲線坐标系通過靈活的坐标線適應複雜幾何問題,是數學、物理和工程中處理非線性或對稱性場景的重要工具。如需進一步了解公式推導或具體案例,可參考向量微積分教材或相關論文。

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