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.

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

    Light-cone coordinate and Lorentz transformation

    Assume that, in cartesian coordinate, we have a quark with momentum ##k=(k_0,0,k_0sin\theta,k_0\cos\theta)## and a fragmented hadron ##p=(p_0,0,0,p_0)##. Define, in light-cone coordinate, ##k^+ = k_0 + k_3 = k_0(1+cos\theta)##, and ##p^+ = p_0 + p_3 = 2p_0##. And the longitudinal momentum...
  2. B

    Global Coord Atlas Universe: GR Coord Charts, Speed Light

    I am wondering how big the local coordinate charts in a coordinate atlas of General Relativity can be. Is it just a few nanometres or all the way to the furthest stars? Also I wonder how the speed of light is defined in GR. Is the velocity defined as the differential with respect to coordinate...
  3. L

    Rotating coordinate system, velocity

    Homework Statement Two coordinate systems xyz (…fixed) and x0y0z0 (moving) coincide at time t = 0. The moving system is rotating about the …fixed z axis, which coincides with z0 axis. The angular velocity is given by ω = tk = tk0. The position vector as measured in the rotational frame is...
  4. H

    Are coordinate operators Hermitian?

    I can't figure this one out given that the coordinate operator is continuous, it's hard to imagine "matrix elements". But presumably since the coordinates of the system (1d free particle) are always real valued, would this make the coordinate operator Hermitian?
  5. A

    Cross products for unit vectors in other coordinate systems

    I am a bit confused often when I have to compute cross products in other coordinate systems (non-Cartesian), I can't seem to find any tables for cross products such as "phi X rho." in spherical I think that these unit vectors are considered to be "perpendicular," so would phi X rho just be "+/-...
  6. S

    Explanation of Equatorial Coordinate System?

    Can anyone explain very clearly(to a n00b like me) right ascension and declination and how to navigate to stars using this system?
  7. S

    Simple coordinate geomety problem

    I'm not sure where to post this. So I'm posting in the General Math section.This is a simple coordinate geometry problem: We have to find the equation of line(s) passing through the point (7,17) and having a distance of 6 units from the point(1,9). Now I'm posting my approach: the equation...
  8. B

    Quote Regarding Choosing A Coordinate System

    Hello everyone, During my linear algebra, my professor had said that a true gentleman never picks a coordinate system, or something along those lines. He alluded to the person who said it, but I did not quite grasp who it was. I was wondering if anyone might know who said this. Thank you.
  9. T

    What are the possible values for the coordinate angles in 3-D space?

    [b]1. Homework Statement [/ In 3-D coordinate space, any two of the coordinate angles must … Select one: a. sum to less than 1 b. be greater than 90° but less than 180° c. each be greater than 45° d. sum to greater than 90° (if they are both less than 90°). e. have cosines less than...
  10. T

    Coordinate angles of three dimensional vectors

    Homework Statement If u know the value of two coordinate angles there is an ulimeted amount of possibility for finding the third coordinate angle A. True B. False Homework Equations The Attempt at a Solution I .not too sure about this one any suggestions would be appreciated I...
  11. T

    Right hand rule three d coordinate system

    Homework Statement If z is up and x is west they y is what direction A. West B. Down C. Up D. East E. South Homework Equations The Attempt at a Solution I tried applying the rule and obtained south as my answer would anyone be able.to provide a.solution
  12. grav-universe

    GR coordinate acceleration problem

    Let's say we have a mass with an object orbitting with constant speed in a circular orbit and a distant observer Bob. According to Bob's coordinate system, the orbit is circular at a speed v and a constant inward coordinate acceleration a. The coordinate acceleration is just what is inferred...
  13. C

    The product of a vector and the length of a polar coordinate

    Homework Statement So I am not sure how to multiply these two (A*R^2) together. Homework Equations A=( x^2 + y^2 + z^2 ) (xe + y e + z e ) Where x represents the three vector compones I also have R^2=x^2+y^2+z^2 The Attempt at a Solution Is the product of A (x^3e + y^3 e + z^3...
  14. J

    Covariant and Contravariant Coordinate

    Hellow everybody! A simples question: is it correct the graphic representation for covariant (x₀, y₀) and contravariant (x⁰, y⁰) coordinates of black vector?
  15. I

    Simple coordinate transformation question

    http://i.imgur.com/MDigPh5.png if i have my original coordinate (white) and i am transforming this into the red coord. , could someone explain to me why y=y'cos\phi is incorrect and why y'=ycos\phi is correct?
  16. M

    A mechanics problem with moving and fixed coordinate systems

    [b]1. A point P is described in terms of a fixed coordinate system XYZ with unit vectors I,J,K and a moving coordinate system xyx with unit vectors i,j,k.at a given instant the location of the origin of the moving system is 80I-90J.the velocity of P relative to moving system is 50i+45j;the...
  17. ShayanJ

    How Do Different Coordinate Systems Affect Vector Operations?

    Recently I've been studying about orthogonal coordinate systems and vector operations in different coordinate systems.In my studies,I realized there are some inconsistencies between different sources which I can't resolve. For example in Arfken,it is said that the determinant definition of the...
  18. B

    Electric Force problem involving HCl and Br- on coordinate axis

    Homework Statement A hydrogen chloride molecule (HCl) has a partial positive charge on the hydrogen atom and a partial negative charge on the chlorine atom. The HCl molecule is placed at A. There will be force on the bromide ion in the +x direction. B. There will be force on...
  19. T

    Stress tensor transformation and coordinate system rotation

    Homework Statement Hi, I am not sure if this is the right place for my question but here goes! The stress tensor in the Si coordinate system is given below: σ’ij = {{-500, 0, 30}, {0, -400, 0}, {30, 0, 200}} MPa Calculate the stress tensor in the L coordinate system if: cos-1a33=45°, and...
  20. R

    Are Oblique Coordinate Systems More Useful Than Orthogonal Systems in 2-D Space?

    In a coordinate system two axes are inclined at an acute angle θ. Is this coordinate system different from a coordinate system in which the axes are inclined at an angle (180 - θ)? if we look at the four quardents in either of the above set of axes, both are included giving the impression that...
  21. D

    Vector components and its coordinate description in a given basis

    Given a basis \mathfrak{B}=\lbrace\mathbf{e}_{i}\rbrace it is possible to represent a vector \mathbf{v} as a column vector \left[\mathbf{v}\right]_{\mathfrak{B}}= \left(\begin{matrix}v^{1} \\ v^{2} \\ \vdots \\ v^{n}\end{matrix}\right) where the v_{i} are the components of \mathbf{v} relative...
  22. T

    Calculating a theta using dot product in 3D coordinate

    I'm so confused about finding an angle, theta in this illustration. With having three coordinate information, how can I calculate the theta using dot product? I would easily find the angle by using trigonometric formula if I ignore the z-axis. But I want to solve this problem with...
  23. mesa

    Use vectors to find coordinate of a point

    Homework Statement So for this problem we are shown a right triangle with point B at (2,1), C at (7,0) and A(x,y). 'A' also happens to rest at the right angle of our triangle. What is the coordinate of 'A' The Attempt at a Solution I tried this one a couple ways. For example the dot...
  24. Rugile

    Derivatives of coordinate equations

    Homework Statement We have two coordinate functions of time, as follows: x(t) = 5 + 2t ; y(t) = -3+3t+2t2. Find velocity \vec{v}, acceleration \vec{a}, tangential acceleration \vec{a_t}, normal acceleration \vec{a_n} functions of time and their magnitude's functions of time. Homework...
  25. C

    Coordinate question - above x-z plane

    Coordinate question -- "above x-z plane" Homework Statement Say I want to verify a condition is true that ∇∇F = 0 above the x-z plane.Where F(x,y,z). Does the "above x-z plane" mean in the x-z plane i.e. we evaluate ∇∇F(x,0,z) ?
  26. D

    Metric for non-inertial coordinate system

    Homework Statement Hey guys. So here's the problem: Consider an ordinary 2D flat spacetime in Cartesian coordinates with the line element ds^{2}=-dt^{2}+dx^{2} Now consider a non-inertial coordinate system (t',x'), given by t'=t, x'=x-vt-\frac{1}{2}at^{2} (1) What is the metric...
  27. E

    Proving The Hamiltonian Is Invariant Under Coordinate Transformation

    Homework Statement (a) Consider a system with one degree of freedom and Hamiltonian H = H (q,p) and a new pair of coordinates Q and P defined so that q = \sqrt{2P} \sin Q and p = \sqrt{2P} \cos Q. Prove that if \frac{\partial H}{\partial q} = - \dot{p} and \frac{\partial H}{\partial p} =...
  28. PsychonautQQ

    Integrating a Semi-Circular Region in Polar Coordinates

    Homework Statement Integrate the double Integral: 6xdydx in polar coordinates The y goes from bottom limit of x(3)^(1/2) to the top limit of (1-x^2)^(1/2) the x goes from 0 to 1/2 Homework Equations The Attempt at a Solution So I graphed it, and it looks like a semi circle on...
  29. E

    Concept of coordinate reference frame in GR

    In SR there is a whole family of so called inertial observers that are defined as those observers that move at relative constant speed with respect to one another, whose descriptions of nature are all equivalent and whose spacetime coordinate are related by Lorentz transformations i.e. those...
  30. H

    Coordinate transformation for line integrals; quadrature rules

    Hi all, The context of this problem is as follows: I'm trying to implement a discontinuous finite element method and the formulation calls for the computation of line integrals over the edges of the mesh. Anyway, more generally, I need to evaluate \int_{e}f(x,y)ds, where e is a line segment...
  31. 2

    Comp Sci [fortran90] cartesian to polar coordinate

    Write a short FORTRAN90 subroutine to convert Cartesian coordinates (x, y, z) to spherical polar coordinates (r, q, f) using • Write a FORTRAN90 program which uses this subroutine to convert the following (x, y, z) coordinates which are read from a text file and stored within a single vector...
  32. D

    Lagrangian where time is a dependent coordinate

    Homework Statement I don't know why I'm having trouble here, but I want to show that, if we let t = t(\theta) and q(t(\theta)) = q(\theta) so that both are now dependent coordinates on the parameter \theta , then L_{\theta}(q,q',t,t',\theta) = t'L(q,q'/t',t) where t' =...
  33. H

    Coordinate and dual basis vectors and metric tensor

    I have been reading an introductory book to General Relativity by H Hobson. I have been following it step by step and now I am stuck. It is stated in the book that: "It is straightforward to show that the coordinate and dual basis vectors themselves are related... "ea = gabeb ..." I have...
  34. B

    Scale Factors via Ellipsoidal Coordinate System Scale Factors

    In Morse & Feshbach (P512 - 514) they show how 10 different orthogonal coordinate systems (mentioned on this page) are derivable from the confocal ellipsoidal coordinate system $(\eta,\mu,\nu)$ by trivial little substitutions, derivable in the sense that we can get explicit expressions for our...
  35. L

    Coordinate systems. Derivatives

    ## \vec{r}=\rho \cos \varphi \vec{i}+\rho \sin \varphi \vec{j}+z\vec{k} ## we get \vec{e}_{\rho}=\frac{\frac{\partial \vec{r}}{\partial \rho}}{|\frac{\partial \vec{r}}{\partial \rho}|} \vec{e}_{\varphi}=\frac{\frac{\partial \vec{r}}{\partial \varphi}}{|\frac{\partial \vec{r}}{\partial...
  36. M

    In proving that the Lagrange equations hold in any coordinate system

    I was checking the proof of this, when things came vague at one point. It goes as follows, how to prove that Lagrange's equations hold in any coordinate system? Answer: Let q_{a} = q_{a}(x_{1},..., x_{3N}, t) here the possibility of using a coordinate system that changes with time is...
  37. P

    Understanding Polar Coordinate Unit Vectors

    Homework Statement The Attempt at a Solution I already know how to do a), but what I am wondering is what the question means by expressing position in the terms of those unit vectors.
  38. K

    Regarding coordinate and non-coordinate bases

    Hello PF members! I have a problem regarding coordinate and non-coordinate bases. As I understood from my course in GR, the partial derivatives of a coordiante system always commute: [\frac{\partial}{\partial x^i}, \frac{\partial}{\partial x^j}] = 0 . Which is not necessarly true for...
  39. Z

    Spherical Coordinate System Interpretation

    Homework Statement (a) Starting from a point on the equator of a sphere of radius R, a particle travels through an angle α eastward and then through an angle β along a great circle toward the north pole. If the initial position is taken to correspond to x = R, y = 0, z = 0, show that its...
  40. P

    Should the Z Coordinate Be Included in XY Plane Vector Problems?

    Hi I didn't post this in homework help, as I didn't feel my question belonged there. If it doesn't belong here, my apologies. I recently took an exam and it turns out I got the first question wrong according to my professor. The problem states: "In the diagram four vectors are represented by...
  41. M

    How to find the X coordinate of a point using trigonometry?

    How to determine the X coordinate of the red point if i know the Y coordinate and the angle between the adjacent side and the hypotenuse in the formed right triangle(see the image)? I don't know the length of the hypotenuse and the adjacent side of the triangle, i know only the angle between the...
  42. M

    2 Rotations on different coordinate systems

    I have a question that i been trying to solve which seam simple but been having trouble. Today I thought about rotation matrix and how the following problem would be solved. Initial Coordinate system (x,y,z) a rotation is desired about x let's say α=30 degrees so that a new coordinate...
  43. D

    Maxwell stress tensor in different coordinate system

    Hi guys, I would like to know if the answer given to this thread is correct https://www.physicsforums.com/showthread.php?t=457405 I got the same doubt, is the expression for the tensor given in cartesian coordinates or is it general to any orthogonal coordinate system? Thanks in advance
  44. Pythagorean

    Insect uses mechanical gears to coordinate jumping

    Insect uses mechanical "gears" to coordinate jumping journalist report: http://www.csmonitor.com/Science/2013/0912/Insect-uses-gears-to-jump-study-finds scientific report: http://www.sciencemag.org/content/341/6151/1254
  45. A

    MHB Coordinate geometry with given parameters.

    Hello, Please forgive me if it's in the wrong sub-forum because don't know where to place it. I need help solving this problem it's chapter 1 and in our class we are already in chapter 5 so I might sound like a fool asking the teacher about it, I was revising and decided to do some questions...
  46. Ibix

    Coordinate charts and open sets

    I have a (probably trivial) question about coordinate charts. I've been studying Sean Carroll's lecture notes on General Relativity. I'm on my second re-read and I'm trying to make sure I understand the basics properly. I hope the terminology is correct - this is my first use. Carroll cites...
  47. L

    How to rotate Cartesian coordinate system?

    Hello, I would like to rotate the Cartesian coordinate system ( i=(1,0,0); j=(0,1,0); k=(0,0,1) ) so that angles between new and the old axes be equal to α, β and γ, respectively. Is any simple way similar to the Euler transformations to accomplish that?
  48. S

    Variance captured in coordinate axis.

    Hi all, Note: The text below is the motivation for my question. To jump to the question immediately, please skip to the line that says HI! I have a set of data points, let's call it A, and I ran principal component analysis to get the top 3 principal components to be able to represent the...
  49. O

    How to do cross product if I have got only two coordinate?

    a =(x,y), b =(h,k) a cross b =? I have idea what to type on google. Is that doing like matrices , a cross b = xk-hy? thanks.
  50. S

    Coulombs force law in a three dimensional coordinate system problem

    Two point charges of Q1 = +37 nC and Q2 = +70 nC are located at points (1,3,0) m and (0,0,2) m, respectively. Q : Calculate the force exerted on Q2 by Q1. Attempt : I applied phythagoras theorem to find the distance between Q1 and Q2, I then applied coulombs force law equation directly...
Back
Top