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Books on the topic 'Curvilinear coordinates'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Antoni, Markus. Calculus with Curvilinear Coordinates. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-00416-3.

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2

Lee, Jong-Hun. Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates. National Aeronautics and Space Administration, 1993.

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3

Lee, Jong-Hun. Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates. National Aeronautics and Space Administration, 1993.

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4

Lee, Jong-Hun. Hypersonic three-dimensional nonequilibrium boundary-layer equations in generalized curvilinear coordinates. National Aeronautics and Space Administration, 1993.

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5

Darboux, Gaston. Leçons sur les systèmes orthogonaux et les coordonnées curvilignes. 2nd ed. Gauthier-Villars, 1991.

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6

Panaras, Argyris G. Boundary-layer equations in generalized curvilinear coordinates. National Aeronautics and Space Administration, Ames Research Center, 1987.

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7

Center, Ames Research, ed. Boundary-layer equations in generalized curvilinear coordinates. National Aeronautics and Space Administration, Ames Research Center, 1987.

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8

Panaras, Argyris G. Boundary-layer equations in generalized curvilinear coordinates. Ames Research Center, 1987.

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9

Panaras, Argyris G. Boundary-layer equations in generalized curvilinear coordinates. National Aeronautics and Space Administration, Ames Research Center, 1987.

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10

Zingg, D. W. A method of smooth bivariate interpolation for data given on a generalized curvilinear grid. [s.n.], 1992.

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11

Yee, H. C. Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates. American Institute of Aeronautics and Astronautics, 1985.

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12

Vysot︠s︡kiĭ, L. I. Geometrizovannai︠a︡ forma uravneniĭ Navʹe-Stoksa. Saratovskiĭ gos. tekhn. universitet, 1995.

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13

Knoblauch, Johannes. Einleitung in die allgemeine Theorie der krummen Flächen. B. G. Teubner, 1991.

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14

H, Carpenter Mark, and Institute for Computer Applications in Science and Engineering., eds. High order finite difference methods, multidimensional linear problems and curvilinear coordinates. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1999.

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15

Ciarlet, Philippe G. An introduction to differential geometry with applications to elasticity. Springer, 2010.

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16

Michelassi, V. Solution of the steady state incompressible Navier-Stokes equations in curvilinear non orthogonal coordinates. von Karman Institute for Fluid Dynamics, 1986.

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17

H, Pletcher Richard, Van Dalsem William R, and United States. National Aeronautics and Space Administration., eds. Wall functions for the k- [epsilon] turbulence model in generalized nonorthogonal curvilinear coordinates: Final report. Heat Transfer Laboratory, Dept. of Mechanical Engineering, Computational Fluid Dynamics Center, Engineering Research Institute, Iowa State University, 1992.

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18

Kumar, Sanjiv. A computer model in general 3-D curvilinear coordinates for the protection of the turbulent flow field in a jet induced ram combustor. National Aerospace Laboratory, 1994.

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19

Cossali, Gianpietro Elvio, and Simona Tonini. Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-49274-8.

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20

Deruelle, Nathalie, and Jean-Philippe Uzan. Curvilinear coordinates. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0003.

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This chapter presents a discussion on curvilinear coordinates in line with the introduction on Cartesian coordinates in Chapter 1. First, the chapter introduces a new system C of curvilinear coordinates xⁱ = xⁱ(Xj) (also sometimes referred to as Gaussian coordinates), which are nonlinearly related to Cartesian coordinates. It then introduces the components of the covariant derivative, before considering parallel transport in a system of curvilinear coordinates. Next, the chapter shows how connection coefficients of the covariant derivative as well as the Euclidean metric can be related to each

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21

Leçons sur les systèmes orthogonaux et les coordonnées curvilignes. 2nd ed. Gauthier-Villars, 1991.

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22

Leçons sur les coordonnées curvilignes et leurs diverses applications. Mallet-Bachelier, 1991.

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23

Antoni, Markus. Calculus with Curvilinear Coordinates: Problems and Solutions. Springer, 2018.

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24

A spectral mulit-domain technique application to generalized curvilinear coordinates. National Aeronautics and Space Administration, Langley Research Center, 1986.

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25

A spectral mulit-domain technique application to generalized curvilinear coordinates. National Aeronautics and Space Administration, Langley Research Center, 1986.

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26

Deruelle, Nathalie, and Jean-Philippe Uzan. Accelerated frames. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0023.

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This chapter shows how, within the framework of special relativity, Newtonian inertial accelerations turn into mere geometrical quantities. In addition, the chapter states that labeling the points of Minkowski spacetime using curvilinear coordinates rather than Minkowski coordinates is mathematically just as simple as in Euclidean space. However, the interpretation of such a change of coordinates as passage from an inertial frame to an accelerated frame is more subtle. Hence, the chapter studies some examples of this phenomenon. Finally, it addresses the problem of understanding what the curvi

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27

Numerical solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates. National Aeronautics and Space Administration, Ames Research Center, 1986.

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28

Numerical solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates. National Aeronautics and Space Administration, Ames Research Center, 1986.

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29

Deruelle, Nathalie, and Jean-Philippe Uzan. Differential geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0004.

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This chapter presents some elements of differential geometry, the ‘vector’ version of Euclidean geometry in curvilinear coordinates. In doing so, it provides an intrinsic definition of the covariant derivative and establishes a relation between the moving frames attached to a trajectory introduced in Chapter 2 and the moving frames of Cartan associated with curvilinear coordinates. It illustrates a differential framework based on formulas drawn from Chapter 2, before discussing cotangent spaces and differential forms. The chapter then turns to the metric tensor, triads, and frame fields as wel

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30

Ciarlet, Philippe G. An Introduction to Differential Geometry with Applications to Elasticity. Springer, 2006.

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31

Ciarlet, Philippe G. An Introduction to Differential Geometry with Applications to Elasticity. CreateSpace Independent Publishing Platform, 2016.

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32

Waleffe, Fabian. Vector and Complex Calculus. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/oso/9780198927839.001.0001.

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Abstract Vector and complex calculus are essential for applications to electromagnetism, fluid and solid mechanics, and the differential geometry of surfaces. The standard multivariable calculus courses are largely limited to `xyz’ calculus, but vector calculus is about geometric concepts invariant under coordinate transformations. This textbook takes the students from the geometry and algebra of vectors, to the key concepts and tools of vector calculus, including differential geometry of curves and surfaces, curvilinear coordinates, and capping off with a study of the essential elements of th

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33

Lim, Hee. Derivation of Del, Gradient, Laplacian, Divergence and Curl of Cartesian and Curvilinear Coordinates: A Simple Basis Preliminary Tensor Mathematics for General Theory of Relativity. Independently Published, 2021.

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34

Inc, Common Core. Eureka Math: A Story of Functions. Wiley & Sons, Incorporated, John, 2015.

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35

Eureka math: A story of functions : Exponential and logarithmic functions. Jossey-Bass, 2015.

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36

Inc, Common Core. Eureka Math: A Story of Functions. Wiley & Sons, Incorporated, John, 2015.

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37

Tonini, Simona, and Gianpietro Elvio Cossali. Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems. Springer International Publishing AG, 2021.

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38

Tonini, Simona, and Gianpietro Elvio Cossali. Drop Heating and Evaporation: Analytical Solutions in Curvilinear Coordinate Systems. Springer, 2020.

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