Coordinates Definition and 1000 Threads

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.

View More On Wikipedia.org
Recent contents Top users
  1. Y

    Coordinates transformation by rotating at the origin.

    I want to transform from rectangular coordinates ( xyz) to (x",y",z") rectangular coordinates that is rotated at the origin as show in the attachment. Then I want to transform (x",y",z") rectangular coordinates into Spherical coordinates. Attach is the method I use, I want to verify I am doing...
  2. C

    MHB Integral - cylindrical coordinates

    Hello, my best problem is about find the integration limits. in cylindrical coordinates- where V is limited by the cylinder y^2+z^2=9 and the planes x = 0, y = 3x and z = 0 in the first octant.
  3. Fernando Revilla

    MHB Integration in polar coordinates

    I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.
  4. N

    Synchronous Coordinates transformation

    Given a specific metric, is there a easy way to transform it in Synchronous coordinates? For example having dsigma2 = (1+z)^2 dt^2 - ds^2 - s^2 dphi^2 - dz^2 , I was able to do some substitutions, but I had to stop at the differential equations presented in the attachement.
  5. Hepth

    Massive Vector Polarizations in Spherical Coordinates

    I can't seem to find one, but does anyone have a reference to the fourvector polarizations for a massive vector particle in spherical coordinates where a momentum is defined as p = \{E, |\vec{p}| \sin \theta \sin \phi, |\vec{p}|\sin \theta \cos \phi , |\vec{p}| \cos \theta\} theta goes...
  6. G

    Comsol 3.5x: Obtaining boundary coordinates from irregular geom obj

    I don't have access to Comsol 4.x. I imported a 3D mesh generated from point cloud data and generated a geometry. (A hollow almost-ellipsoid.) I solve my system on the surface/boundary alone; there is no volumetric data. I need to extract 1D data from the surface/boundary at points other...
  7. M

    Kruzkal Coordinates Inside Horizon: Defining u', v

    We start by defining two coordinates ##u=t+r^*## and ##v=t-r^*##. Then we define another two coordinates ##u'=e^{u/4GM}## and ##v'=-e^{-v/4GM}##. But from what I have understood this is true for ##r>2GM##. How do we define ##u'## and ##v'## for ##r<2GM##? I think it's ##u'=e^{u/4GM}## and...
  8. A

    Change of variables from one set of coordinates to another in Fourier

    ... ... I am curious to know why we have to multiply with e^{-j\omega t} in Fourier transform? What is the purpose of this? I have heard somewhere that the transform is merely a change of variables from one set of coordinates to another. I would like to know more about this. Can you help me?
  9. V

    Velocity Vector in Polar Coordinates (Kleppner p.30)

    In polar coordinates we have \vec{r} = r \hat{r} \Rightarrow \vec{v} = \frac{d}{dt}({r \hat{r}}) = \dot{r}\hat{r} + r \frac{d \hat{r}}{dt} . In the book Introduction to Mechanics, K & K says the right term is the component of velocity directed radially outward. (Surely a typo, as the left...
  10. S

    How to translate from polar to cartesian coordinates:

    How to translate r = 2 /(2 - cos(theta)) to cartesian coordinates: so far: r = 2 /(2 - cos(theta)) r = 2 /(2 - cos(theta)) |* (2 - cos(theta)) both sides r (2 - cos(theta))= 2 2*r - rcos(theta) = 2 | know x = rcos(theta) 2*r - x...
  11. J

    Line integral around a circle in polar coordinates

    I know that \oint_{C}\mathrm{d}\vec{l} = 0, for any closed curve C. But when i try to calculate the integral around the unit circle in polar coordinates, I get a result different from zero. Here is my approach : \oint_{C}\mathrm{d}\vec{l} = \int_{0}^{2\pi}\hat{\phi}\mathrm{d}\phi =...
  12. O

    Electron in Constant B-Field (Cylindrical Coordinates)

    Homework Statement The position of a proton at time t is given by the distance vector \vec{r}(t) = \hat{i}x(t) + \hat{j}y(t) + \hat{k}z(t) A magnetic induction field along the z-axis, \vec{B} = \hat{k}B_{z} exerts a force on the proton \vec{F} = e\vec{v}\times\vec{B} a.) For...
  13. S

    Projection of a distance in rectangular coordinates

    My problem is that I believe I have a wrong concept somewhere, and I can't find what I'm doing wrong exactly. For this problem let's suppose what I want to do is find the rectangular coordinates of BC. I had two "possible solutions" I tried to achieve this, . First the correct one: (I...
  14. I

    How to evaluate this nabla expression in spherical coordinates?

    I'm currently working out the Schrödinger equation for a proton in a constant magnetic field for a research project, and while computing the Hamiltonian I came across this expression: (\vec{A}\cdot\nabla)\Psi where \Psi is a scalar function of r, theta, and phi. How do you evaluate this...
  15. D

    Vector calculus for ellipse in polar coordinates

    Hello =] I'm having trouble with this question, can somebody please help me with it! I'll thanks/like your comment if help me =) ![Question][1] I know that for a ellipse the parametric is x=a sin t , b= b cos t t:0 to 2pi (?) for part a) I drew up the graph but not sure if it's...
  16. M

    How do spherical coordinates work for finding volume in a given region?

    Homework Statement Find VR_{z}^{2} = \int \!\!\! \int \!\!\! \int_{E} (x^{2} + y^{2})dV given a constant density lying above upper half of x^{2}+y^{2} = 3z^{2} and below x^{2}+y^{2}+z^{2} = 4z.Homework Equations The Attempt at a Solution Why does it say upper half of x^{2}+y^{2} = 3z^{2}? It's...
  17. D

    Coordinates of centre of mass of lamina

    An industrial tool is made from alaminar material occupyingthe region between thestraight lines y =2, y=1 2x and y =3−x. The density of thematerial varies and is given by thefunction σ(1 + x), where x is the horizontal distancefrom the y-axis and σ is aconstant. The mass of the...
  18. N

    Area integral with cylindrical coordinates

    Homework Statement find the area of the surface defined by x2+y2=y, with yE[0,4] The Attempt at a Solution I tried setting it up with cylindrical coordinates, but it doesn't work. Why? ∫40∫2pi0r*dθ*dy, where r=√y Is it because my height, dy, has a vertical direction while its...
  19. M

    Change of variables cylindrical coordinates

    Homework Statement Let S be the part of the cylinder of radius 9 centered about z-axis and bounded by y >= 0; z = -17; z = 17. Evaluate \iint xy^2z^2 Homework Equations The Attempt at a Solution So I use the equation x^2 + y^2 \leq 9, meaning that r goes from 0 to 3 Since y...
  20. mnb96

    Inner product in curvilinear coordinates

    Hello, let's assume we have an admissible change of coordinates \phi:U\rightarrow \mathbb{R}^n. I would like to know how the inner product on ℝn changes under this transformation. In other words, what is \left\langle \phi (u), \phi (v) \right\rangle for some u,v \in U ? I thought that...
  21. W

    Converting Cartesian to Polar Coordinates: Explained with Example

    Homework Statement Find polar coordinates. Homework Equations Cartesian: (-3,4) The Attempt at a Solution r = sqrt(9+16) = 5 sinθ = 4/5 cosθ = -3/5 θ = ∏ - arctan(4/3) Answer: (5, ∏ - arctan(4/3)) I do not understand why we have subtracted the value arctan(4/3) from pi?
  22. B

    How to find an equation with multiple x,y coordinates

    Hi, I tried using geogebra to find an equation that exactly goes through the list of points I plotted on the graph but I failed to find any way so far. I have tried using, FitExp, FitGrowth, and Fitline, and so far none of them worked. I have no idea what kind of equation this is so I cannot...
  23. X

    Curve C is given in Polar Coordinates by the equation r=2+3sin(theta)

    Homework Statement Curve C is given in Polar Coordinates by the equation r=2+3sinθ. Consider the usual Cartesian plane and take O as the pole and the positive x-axis as the polar axis. Find points on the curve C where the tangent lines are horizontal or vertical and sketch the curve C...
  24. quasar987

    Jacobi identity in local coordinates?

    Jacobi identity in local coordinates?!? Apparently (i.e. according to an article written by physicists), the Jacobi identity for the Poisson bracket associated to a Poisson bivector \pi = \sum\pi^{ij}\partial_i\wedge\partial_j is equivalent to...
  25. E

    Triple Integration from Rectangular to Spherical Coordinates

    Homework Statement Convert the integral from rectangular coordinates to spherical coordinates 2 √(4-x^2) 4 ∫ ∫ ∫ x dz dy dx -2 -√(4-x^2) x^2+y^2 Homework Equations x=ρ sin∅ cosθ y=ρ sin∅ cosθ z=ρ cos∅ In case the above integrals cannot be understood: -2...
  26. baby_1

    Convert Cartesian coordinates to spherical shape

    Hello how can Convert Cartesian coordinates to spherical with shape? for clear my question i explain a way to convert my coordinates in different spherical. for example i use this diagram to convert Cartesian coordinates to Cylindrical(with image to axises) for example: now how can i do...
  27. V

    How Do You Calculate Time Along a Path in Polar Coordinates?

    Homework Statement I have a path defined in polar coordiantes defined as r=a*cos2(θ). I also have the velocity along this path as a function of θ. I want to find the time take to move between two given angles on the path.2. The attempt at a solution I know that this problem will involve some...
  28. C

    How can velocity be expressed as a function of time in polar coordinates?

    Homework Statement Here is a picture of the situation http://i48.tinypic.com/vnmi5t.jpg Homework Equations polar coordinate system The Attempt at a Solution ok so first I'm attempting to find velocity as a function of time, first I know V=(dR/dt)er +(R)(d∅/dt)e∅ - this is a...
  29. C

    MHB Why Is the Maximum Radius Not sqrt(2) When Converting to Polar Coordinates?

    Hellow MHB, I'm trying to understand how can i pass this integral to polar coordinates. My biggest doubt is about the "radius".
  30. X

    Ekman Surface Pumping in Polar Coordinates?

    Hello, I am working on a question in a GFD textbook about tea leaves collecting in the center of the cup regardless of the direction that the tea is stirred. I have an idea of why this is the case but to prove it I need to convert the equation for Ekman pumping to polar coordinates. Its given...
  31. F

    Cross product in cylindrical coordinates

    In my physics textbook we have d\vec{l}=\hat{z}dz and then it says d\vec{l}\times \hat{R}=\hat{\phi}\sin \left (\theta \right )dz How so? What is \hat{z}\times\hat{R}? If it is \hat{\phi} then where does the sine come from?
  32. M

    Laplacian in Slanted Coordinates

    Whoops, I figured it out!
  33. P

    A novel way of defining coordinates?

    Let's start with the motivation - I'm trying to think of ways to talk about building coordinate systems operationally, ideally without directly using ideas like "space like geodesics" that one needs for fermi-normal coordinates. The ideas behind geodesics don't strike me as terribly...
  34. X

    A question about Jacobian when doing coordinates transformation

    Hi, When I do the following transformation: $$ X_1=x_1+x_2 \\ X_2=x_2 $$ It turns out that the Jacobian ##\partial (X_1,X_2)/\partial (x_1,x_2)## is 1. But we have: $$ dx_1dx_1+dx_1dx_2=d(x_1+x_2)dx_2=dX_1dX_2=|\partial (X_1,X_2)/\partial (x_1,x_2)|dx_1dx_2=dx_1dx_2 $$ So we...
  35. J

    Spacecraft path with polar coordinates

    There is a circular gate rotating at a constant angular speed of ω. The circular gate has a tunnel across its diameter. The mission is to pass through the gate. (That is, come in one side of the gate, travel the whole diameter, and exit at the other side.) Also, craft is neutrally buoyant...
  36. A

    Meaning of Schwarzschild solution in isotropic/anisotropic coordinates

    According to the Schwarzschild solution in the most common anisotropic (Schwarzschild?) coordinates the proper time and the coordinate time are related as...
  37. B

    Calculating Impedances in Polar Coordinates: Tips and Tricks

    Hello all i have a question about adding 3 impedances given in polar form, must i convert them to x..y.. first or is there a quicker way on a calculator and if so can anyone give advice i have the equation Zo=√Z(oc)Z(sc) but finding it hard to understand many thanks.
  38. S

    Determining whether grid coordinates lie within a circle

    I have a grid and want to determine whether a point lies within (our outside of) a circle. The grid cells simply have integer coordinates, e.g. x = 5, y = 7. The circle's radius is known, and also an integer value. I wrote a program that can place points in a (quantized) circle using...
  39. Petrus

    MHB Coordinates of Hexagon Vertices in Base (AC, AD)

    Consider a regular hexagon ABCDEF (in order counterclockwise). Determine the coordinates of AB, AE AND AF (->) in the base (AC, AD) (->) AB(->)=(_____,_____) AE(->)=(_____,_____) AF(->)=(_____,_____) what I mean with exemple AF(->) positive way from A to F. I have draw a it but I got problem...
  40. S

    Changing the Gaussian Distribution from cartesian to polar coordinates

    Homework Statement "You are now going to show that, in the Gaussian distribution P(x)=Ae^(-Bx^2) the constant A is equal to sqrt(B/Pi). Do this by insisting that the sum over probabilities must equal unity, Integral(P(x)dx)=1. To make this difficult integral easier, frst square it then combine...
  41. S

    How Do You Find Alternate Polar Coordinates with Different Signs for R?

    Homework Statement Find two other pairs of polar coordinates of the given polar coordinate, one with r > 0 and one with r < 0. Then plot the point. (2, 5π/3)Homework Equations I don't there are any. The Attempt at a Solution I'm not completely sure of how to do this actually. I know that...
  42. skate_nerd

    MHB Evaluating a double integral in polar coordinates

    I've done this problem and I have a feeling it's incorrect. I've never done a problem like this so I am kind of confused on how else to go about doing it. The goal is to change the cartesian integral $$\int_{-a}^{a}\int_{-\sqrt{a^2-x^2}}^{\sqrt{a^2-x^2}}\,dy\,dx$$ into an integral in polar...
  43. T

    Patch of a surface in spherical coordinates?

    Homework Statement I am currently trying to prove: S = ∫∫a2sinΦdΦdθ Here is my work (note that in my work I use dS instead of S, this is an accident): I end up with: S = ∫∫a*da2sinΦdΦdθ Where da is the infinitesimal thickness of the surface. Why am I getting the wrong answer?
  44. N

    Normal and Tangential Coordinates

    Homework Statement The 2-oz bead P is given an initial speed of 5 ft/sec at point A of the smooth guide which is curved in the horizontal plane. The horizontal force between the bead and the guide has a magnitude of 3 oz at point B. Determine the radius of curvature ρ of the path at this...
  45. LunaFly

    Double integral of arctan in polar coordinates

    Homework Statement Evaluate the integral using polar coordinates: ∫∫arctan(y/x) dA Where R={ (x,y) | 1≤ x2 + y2 ≤ 4, 0≤y≤x Homework Equations X=rcos(T) Y=rsin(T) r2=x2 +y2 The Attempt at a Solution First thing was drawing a picture of R, which I think looks like a ring 1 unit thick...
  46. N

    Metric constraints in choosing coordinates

    Hello all, I've been puzzled by this problem for some time now and was wondering if anyone here could help me out. Textbooks on GR (specifically when going into gravitational waves) tend not to elucidate this. It's often taken for granted that through the gauge diffeomorphism invariance (or...
  47. N

    What's the Maximum Observation Time Without Rotating the Dome?

    Homework Statement Astronomer observing the sky with a small telescope by hole at the observatory in the middle of dome (lens diameter is much smaller than the diameter of the dome). Calculate the maximum time when astronomer can still observe objects near the celestial equator, without having...
  48. W

    Cylindrical coordinates of line through a point?

    Homework Statement Use cylindrical coordinates to describe the line through the point (1,1,0) and parallel to the z-axis. Homework Equations How does one go about this? Even my course book was unclear about this. Any general overview about how to do such a question will be helpful. The...
  49. A

    Surface Area of a Sphere in Spherical Coordinates; Concentric Rings

    Hey, folks. I'm trying to derive the surface area of a sphere using only spherical coordinates—that is, starting from spherical coordinates and ending in spherical coordinates; I don't want to convert Cartesian coordinates to spherical ones or any such thing, I want to work geometrically...
  50. M

    Kinetic Energy in Spherical Coordinates

    Homework Statement Derive the expression for kinetic energy of a classical particle in spherical coordinates. Homework Equations I believe the answer I am supposed to reach is: T=\frac{1}{2} m (\dot{r}^2 + r^2\dot{\theta^2} + r^2\dot{\phi ^2}sin^2\theta) The Attempt at a Solution...
Back
Top