What is Coordinate: Definition and 908 Discussions

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

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  1. N

    Cylindrical coordinate sysyem-Gambit

    hi, i am doing a simulation of 3D problem.i want to draw it cylindrical coordinate sysyem(r,z, o).but gambit shows X , Y , Z Coordinate . how to do in cylindrical co ordinate , will it show r, z and o axis ? i opened the Tools command button then i changed the co ordinated system to...
  2. S

    Differential Geometry: Coordinate Patches

    Sorry i wasnt able to get help in the homework department. figured id try here. Homework Statement For a coordinate patch x: U--->\Re^{3}show thatu^{1}is arc length on the u^{1} curves iff g_{11} \equiv 1 The Attempt at a Solution So i know arc legth of a curve \alpha (t) =...
  3. S

    Differential geometry: coordinate patches

    Homework Statement For a coordinate patch x: U--->\Re^{3}show thatu^{1}is arc length on the u^{1} curves iff g_{11} \equiv 1 The Attempt at a Solution So i know arc legth of a curve \alpha (t) = \frac{ds}{dt} = \sum g_{ij} \frac {d\alpha^{i}}{dt} \frac {d\alpha^{j}}{dt} (well that's actually...
  4. S

    Coordinate independence of Lie derivative

    Hello Forum, since my GR tutor can't help me with some issues arising I thought it is time to register here. I am very confused about the phrase "coordinate independence". Especially regarding the Lie Derivative and the Commutator of two vector fields. 1) The Lie Derivative is said...
  5. B

    Coordinate Distance Calculation

    Homework Statement When you have a point in \Re3, like for example let J(3, 7, 3) and Q(1, 2, 3). What is the distance in terms of coordinate between them? Like can you just subtract the corresponding components? Homework Equations I am not sure if it only works for the formula...
  6. G

    About the shperical coordinate

    Here I am doing a spherical pendulum problem, and i was asked to represent the unit vectors of spherical coor in terms of Cartesian coor, which i have already solved: r=sinθcosφ i + sinθsinφ j + cosθ k θ=cosθcosφ i + cosθsinφ j - sinθ k φ= -sinφ i + cosφ j where φ is the angle on the X-Y...
  7. Z

    Rotation of coordinate system mistake or paradox?

    Hello to all, I am currently studying computer graphics and I have came up with the following problem. Consider that we have three coordinate systems, let's say CSA1, CSA2 and CSA3 that have the same origin and differ by a rotation. That is to CSA2 connects to CSA1 by R12 and CSA3 to CSA1 by...
  8. Z

    Is the hamiltonian in the coordinate representation always diagonal?

    In the coordinate representation of a quantum mechanical system, is it always true that the Hamiltonian of the system is diagonal? If so, can someone explain to me why this is true?
  9. M

    Latitude-longitude coordinate range given radius

    Hello, Is there a formula for calculating a range of latitude-longitude coordinates within a certain radius of a given point? Using ellipsoidal geometry, preferably.
  10. B

    Vector analysis in cylindrical coordinate system

    if a point in cylindrical cordinates is A=(r1,\theta1,z1) and another point is B=(r2,\theta2,z2) (if ar,a\theta,az are unit vectors) then the position vector of A is = r1<ar>+\theta1<a\theta>+z1<az> and the position vector of B is = r2<ar>+\theta2<a\theta>+z2<az> so vector BA=...
  11. O

    What Are the Timelike and Null Coordinates Used in the Schwarzschild Metric?

    Now I'm study the Schwarzschild geometry from "General Relativity (M.P. Hobson)". Since the Schwarzschild metric has coordinate singularity at r=2M so to remove this singularity they use the Eddington-Finkelstein coordinate, first they begin with introduces new time parameter "p" p=ct+r+2M...
  12. X

    Understanding Polar Coordinate Integration

    can someone explain to me why my teacher divided the area into two? I=\int1,0\int(2x-x^2)^.5,0 1/(x^2+y^2)^.5dydx ugggggh i tried to use the latex... anyway... he used the polar coordinate to do this. once he turned it into polar coordinate, he divided the area into 2 bounded by (pi/4 - o...
  13. V

    Is the Time Coordinate Timelike or Spacelike?

    Sorry, I do realize that this is probably a really stupid question, but can someone please help me understand the following statement: My understanding of a timelike path, is one which always stays inside a light cone, defined by lines with gradients c and -c that cross at the origin...
  14. A

    The coordinate ring - Algebraic geometry

    I'm looking for help understanding the coordinate ring. The definition I have roughly says There is a surjection PI:k[t_1 , ... , t_n] ---> k[X] given by restricting a polynomial to X, where X is an algebraic set. Then k[X] is called the coordinate ring. As i understand it all...
  15. G

    Linear Transformation / Coordinate Vector Question

    Homework Statement The following vectors form an ordered basis E = [v1, v2] of the subspace V = span(v1,v2): v1 = (1,2,1)^T , v2 = (3,2,1)^T. The vector v = (24,-8,-4)^T belongs to the subspace V. Find its coordinates (c1,c2)^T = [v]E relative to the ordered basis E = [v1,v2]. Homework...
  16. C

    Can the Minkowski Line Equation Explain Time Dilation in Special Relativity?

    Hey If you have the Minkowski line equation of -ds^2 = c^2 d tau^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 I don't understand how you can assume from this ^ that each observer in different reference frames will experience time changing at the same rate 'dt'. I thought that tau was the relative...
  17. H

    Linear Transformations and Coordinate

    Homework Statement Let B be a basis of R^2 consisting of the vectors <5,2> and <1,5> and let R be the basis consisting of <2,3> and <1,2> Find a matrix P such that [x]_r=P[x]_b for all x in R^2 Homework Equations Ax=B? The Attempt at a SolutionI attempted by using Ax=B as a format to solve...
  18. T

    Coordinate on sphere(vector calculus)

    I have a sphere, with center x0,y0,z0 and a radius r. Furthermore I have a point 1 outside the sphere x1,y1,z1. But now I want to calculate the coordinates of Point 2, which is on the surface of the sphere, and the CenterP2P1 is 90 degrees there. With these two points known points (Center...
  19. A

    Vector components for custom coordinate axes

    I'm having trouble finding information online regarding figuring out vector components when you set up your own axes. All examples just show a basic x-y coordinate system where the cos and sin components of the vector are obvious. However, suppose you have a problem where, for example you have...
  20. G

    Coordinate vector basis proving question

    Homework Statement Let S = {v1,v2,...,vn} be a basis for an n-dimensional vector space V. Show that {[v1]s,[v2]s,...[vn]s} is a basis for Rn. Here [v]s means the coordinate vector with respect to the basis S. Homework Equations [v]s is the coordinate vector with respect to the basis S...
  21. A

    Random Coordinates: How to Randomize a Position on a Sphere

    How do i randomize a position on a sphere? Using a random number between 0 and 360 for longitude and a number between -90 to 90 for latitude would make it more probable to get closer to the poles right?
  22. C

    Looking for a coordinate system

    I'm working with a cartestian system that has certain periodic properties I'd like to exploit with a new coordinate system, but I don't know one that would work. The trajectory of the state of the system is symmetric across non-adjacent squares (ie a checkerboard of sorts), so that (x,y) can...
  23. B

    VERY SIMPLE Coordinate Geometry

    Homework Statement Using the concept of equal slopes, state whether the following sets of points are collinear or not A(5, -6) B(0, -1) C(-4, 3)Homework Equations Slope = vertical rise/horizontal runThe Attempt at a Solution I only got as far as... 5-0/-6+1 = 5/-5 I think what I just did...
  24. I

    Coordinate transformation and conformal transformation?

    I'm confused by the relation of coordinate transformation and conformal transformation. I found a nice note about conformal field theory written by David Tong. It does contain the demonstration related to my question, but I still don't understand. Here it goes, The definition of conformal...
  25. S

    Astrophysics Coordinate Questions

    Homework Statement A sailor somewhere on the Pacific Ocean uses a navigational instrument to measure the altitude of the star Aldebaran (α Tauri, the brightest star in the constellation Taurus, the Bull) at the moment that Aldebaran is due south of the zenith. The equatorial coordinates of...
  26. M

    What Is the Epoch Time for the WGS84 Coordinate System?

    Hello, I've been searching all over for the epoch time of the WGS84 coord system. A GPS I'm using says its 06/01/1980, but I don't know if starts from 12:00:00 ET. Is there an epoch by definition or is it arbitrary?
  27. D

    Coordinate systems in the solar system?

    I have read the wikipedia page regarding Celestial coordinate systems and searched on google, but I cannot find any coordinate systems which describe a planet's position in it's orbit. Does there exist such a system? An example use of this system would be in locating the planets in the sky. I...
  28. L

    Parametrization vs. coordinate system

    I am reading Differential Topology by Guillemin and Pollack. Definition: X in RN is a k-dimensional manifold if it is locally diffeomorphic to Rk. Suppose U is an open subset of Rk and V is a neighborhood of a point x in X. A diffeomorphism f:U->V is called a parametrization of the...
  29. B

    X Coordinate in Electric Field System

    Homework Statement Locate the x coordinate such that E=0? Coulomb constant is 8.98755x10^9 N m^2/C^2. The 1.68x10^-6 charge is at the origin and a -8.54x10^-6 charge is 10 cm to the right, as shown in the figure. http://i325.photobucket.com/albums/k398/bdh1613/018.jpg Locate the x...
  30. J

    Understanding the 3 coordinate systems for a Schwarzschild geometry

    Hello, There are 3 main coordinate systems for a Schwarzschild geometry : Lemaitre-Rylov (LR), Eddington-Finkelstein (EF), Kruskal-Szekeres (KS). Thanks to my readings, I know thaht KS coordinates are better than EF coordinates and that EF coordinates are better than LR coordinates. But, I...
  31. Rasalhague

    Coordinate Transformation & Jacobian Matrix

    Is the following correct, as far as it goes? Suppose I have a vector space V and I'm making a transformation from one coordinate system, "the old system", with coordinates xi, to another, "the new system", with coordinates yi. Where i is an index that runs from 1 to n. Let ei denote the...
  32. P

    Galilean Coordinate Transformation (Classical Relativity)

    Homework Statement An observer in an inertial reference frame S sees two cameras flash simultaneously. The cameras are 800 m apart. He measures that the first flash occurs at four coordinates given by X1=0, Y1=0, Z1=0 and T1=0, and that the second flash occurs at four coordinates given by...
  33. B

    Converting partial derivatives between coordinate frames

    Homework Statement Given Cartesian coordinates x, y, and polar coordinates r, phi, such that r=\sqrt{x^2+y^2}, \phi = atan(x/y) or x=r sin(\phi), y=r cos(\phi) (yes, phi is defined differently then you're used to) I need to find \frac{d\phi}{dr} in terms of \frac{dy}{dx} Homework...
  34. M

    Coordinate Transformations Question

    Hi there. This isn't so much a math question as it is a conceptual question. I can't seem to wrap my head around the need for coordinate transformations. *Why* do they need to be done? I think I really need a picture for this, so this might not be the right place to ask, but if you can...
  35. Q

    Left-Handed Coordinate System: Unit Vectors i,j,k

    A friend asked me this question today. It kinda threw me for a loop. The cartesian coordinates system is a left handed coordinate system right, so therefroe they are defined by a left handed coordinate syste correct?
  36. Rasalhague

    Coordinate Chart on Manifold: What is $\mathbb{R}^{n}$?

    In defining a coordinate chart, \left ( U,\phi \right ), U \in M, \phi : U \to \mathbb{R}^{n}, on a manifold M, what exactly is \mathbb{R}^{n}: the set of all n-tuples, a topological space, a metric space, a vector space, Euclidean space conceived of as an inner product space, Euclidean...
  37. N

    Griffiths E&M 3.33 write e-field of dipole moment in coordinate free form

    Homework Statement Show that the electric field of a "pure" dipole can be written in the coordinate-free form E_{dip}(r)=\frac{1}{4\pi\epsilon_0}\frac{1}{r^3}[3(\vec p\cdot \hat r)\hat r-\vec p]. Homework Equations Starting from E_{dip}(r)=\frac{p}{4\pi\epsilon_0r^3}(2\cos \hat r+\sin\theta...
  38. J

    Volume of tetrahedra formed from coordinate and tangent planes

    I have that P is the tangent plane to the surface xyz=a^{3} at the point (r,s,t). I need to show that the volume of the tetrahedron, T, formed by the coordinate planes and the tangent plane to P is indepedent of the point (r,s,t). I have found that P is; \frac{x}{r} + \frac{y}{s} +...
  39. K

    HELP Setting up triple integral in spherical coordinate

    HELP! Setting up triple integral in spherical coordinate Homework Statement http://img517.imageshack.us/img517/9139/83291277.jpg Homework Equations I set up the bound for this problem as following: r=0..2/cos(phi), phi=pi/2..3pi/4, theta=0..2pi, but maple always return an error in...
  40. S

    Coordinate systems for electric fields.

    Im curious about an electric field (somewhere of radius s) inside a solid sphere (radius a) such that: \int E.da=E4\pi s^{2} and Q = \frac{\rho 4\pi s^{3}}{\epsilon_{o}3} What is the difference between using each coordinate system to solve for E? It's just that I've really had to teach...
  41. T

    Another coordinate conversions.

    Homework Statement The actual question is to evaluate the integral. All I need help on is the setting up part. Instead of making a thread for each, I will post 3 integral question with my attempts. Just tell me if you see something wrong from rectangular to spherical conversion...
  42. T

    Changing from rectangular coordinate to sperical

    Homework Statement change from rectangle to spherical coordinate : z^2 = x^2 + y^2 I know that : z = pcos(phi) x = psin(phi)cos(theta) y = psin(phi)sin(theta) there fore z^2 = x^2 + y^2 in spherical coordinate is p^2cos(phi)^2 = (psin(phi)cos(theta))^2 +...
  43. T

    Help Rectangle to Cylindrical coordinate question

    Homework Statement evaluate : \int\int\int_{E} e^z DV where E is enclosed by the paraboloid z = 1 + x^2 + y^2 , the cylinder x^2 + r^2 = 5 I just need help setting this up. I know that theta is between 0 and 2pi Now is z between 0 and 1 + r ? and r is between 0 and sqrt(5)...
  44. T

    Rectangle to Cylindrical coordinate question

    Homework Statement can you explain this conversion, I am not sure. Rectangle coord : \int^{2}_{-2}\int^{sqrt(4-x^2)}_{-sqrt(4-x^2)}\int^{2}_{sqrt(x^2 + y^2 )} F(x) dzdydx = cylindrical coord : \int^{2\pi}_{0}\int^{2}_{0}\int^{2i}_{r} r*dzdrd\theta I see that x^2 + y^2...
  45. R

    Linear Algebra: Coordinate system corresponding to the basis

    Homework Statement In the xy-plane, sketch the coordinate system [ a; b] corresponding to the basis { (1, 1 ) , (1, -1) } by drawing the lines a = 0, \pm1 and b = 0, \pm1. What point in the xy-plan corresponds to a = 1, b = 2?Homework Equations Not sure of any in this caseThe Attempt at a...
  46. O

    Curved spacetime and imaginary coordinate

    In Misner, Thorne, Wheeler: "Gravitation" it is stated on that "no one has discovered a way to make an imaginary coordinate work in the general curved spacetime manifold" (p.51). Can anyone elaborate on this? Right now, I don't get why it wouldn't work and nothing more is said in the book.
  47. D

    Magnetic field expansion in cylindrical coordinate

    Homework Statement Dear all, i am figuring the taylor expansion for magnetic field in cylindrical coordinate (r,theta,z). The taylor expansion is simple, however if i want to express the magnetic field in just z direction, i don't know to start. It is because i seen some books...
  48. M

    Pendulum in polar coordinate system problem

    Homework Statement A pendulum consists of a particle of the mass m and a thread of the length l (we don't consider the threads mass). The acceleration caused by gravity is g. Solve the particles displacement and the force caused by the tension in the thread T in a polar coordinate system. The...
  49. 1

    Help with integrating polar coordinate equations

    Homework Statement I need to integrate the equation shown below in the picture. It is a polar coordinate function with r(double dot) being the acceleration radial and theta(double dot) being angular acceleration. I need to integrate with respect to time, to get equations for r(dot) and r...
  50. S

    Understanding Coordinate Transforms: Partial Derivatives

    Hey, I am having trouble understanding how you can transform one set of coordinates into another using partial derivatives i just don't get the whole thought process behind it. I came across this while reading about covariant and contrivariant vectors. If anyone can help clear up how this works...
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