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. DrGreg

    Removing the Schwarzschild coordinate singularity

    I'm creating this thread to discuss some issues raised by kev in the Understanding maximally extended Schwarzschild solution thread, to avoid diverting that thread from its original question. As any fule kno, the problem with Schwarzschild coordinates is their coordinate singularity at the...
  2. C

    How Do You Calculate Point P3 in a Coordinate System with a 90-Degree Angle?

    See the attached image first. Given that I know points P1 and P2, what would the equation be to get point P3, given that the angle is 90 degrees and the distance from P2 to P3 is 1/5 the distance from P1 to P2? Thanks in advance!
  3. G

    Coordinate transformations Spherical to Cartesian

    Hi, I would like to transform a vector from Spherical to cartesian coordinate system. But the question is probably not that straight forward. :( I have a vector say E = E_r~\hat{r}+E_{\theta}~\hat{\theta}+E_{\phi}~\hat{\phi}. But I know only the cartesian coordinate from where it...
  4. K

    Del operator in different coordinate

    Homework Statement I would like to transform the Del operator form rectangular coordinate system to spherical coordinate system. The find the Laplace operator in spherical coordinate. 2. The attempt at a solution 1) In rectangular coordinate system, Del operator is given by \nabla =...
  5. K

    About momentum operator in other coordinate system

    Hi there, does anyone know where can I found a material or note about how to deduce momentum operator in coordinate system other than linear coordinate (especially in spherical coordinate system)? Thanks in advanced.
  6. M

    Coordinate Transformations in GR

    As I try to understand GR, I find coordinate transformations just about everywhere. My question is simply: What is the reason coordinate transformations play such an important role in GR? Thanks.
  7. J

    How are tensors transformed in non-linear coordinate systems?

    Let's say I have a non-linear transformation for (ct,x,y,z) in one coordinate system to (cT,X,Y,Z) of another coordinate system. Despite being nonlinear, I assume I can transform all four-vectors using the same non-linear transformation (correct?), but how in the world do I transform the...
  8. S

    Find the X coordinate with slope of -2

    Homework Statement Function defined as: y = The integral from 0 to x2 of 1 / (1 - Sqrt(t) + t) There exists a point where the slope of the tangeant is = -2. Find the x coordinate at this point. Homework Equations Fundemental Theorem of Calculus The Attempt at a Solution...
  9. stevebd1

    Integrating Gullstrand-Plainleve Coordinates in Kerr Metric

    I'm looking at Gullstrand-plainleve coordinates in Kerr metric. While on the whole, it seems pretty straight forward, I found the integral aspect a little inaccessible. I've had a look at various web pages regarding integrals but to be honest, I don't know where to start with the following. Any...
  10. C

    How Do Coordinate Frames Influence Equations in Wind Generator Dynamics?

    Homework Statement This is a basic question to a kind of complex problem, any help will be deeply appreciatted. I have all the motion equations for the system described below, but i have a problem with the reference frames... So the problem is as follows: A small wind generator is protected...
  11. Jonathan Scott

    Schwarzschild solution radial coordinate and black holes

    When people appear to be getting very confused about the weird nature of black holes, I normally respond with answers based on standard black hole theory, but I sometimes feel I should also call attention to the point that some people now think that the "black hole" solutions to the...
  12. N

    Laplace equation in polar coordinate

    Urr+(1/r)*Ur+(1/r^2)*Uθθ=0 a<r<b, 0<θ<w with the conditions U(r,0)=U1 U(r,w)=U2 U(a,θ)=0 U(b,θ)=f(θ)
  13. K

    How to convert cylindrical coordinate to cartesian coordinate?

    Homework Statement Cylindrical: (5,5,53.2) Cartesian = ?? How bout Cartesian to coordinate? Any websites that shows all the conversions?
  14. S

    Coordinate Systems in Modern Interpretation of Relativity

    Hello, I've really been enjoying reading these forums the last couple of weeks, and finally decided to register to ask a question. This is an earnest question about what the modern interpretation is, and how I and another student of relativity can learn more about the modern understanding...
  15. B

    Coordinate (1,-2), angle of intersection thru origin?

    I'm trying to do a simple electric field due to point charges problem, but I'm stuck on a very simple detail. There are a number of point charges on an xy plane, and one of the point charges is at the cooridinate (1,-2). I need to figure out which angle a line drawn from this point to the...
  16. S

    Graphing Coordinate Systems in R3: Spherical Equations and Inequalities

    Homework Statement Graph the surface in R3 Homework Equations Spherical equation \rho = 2asin(\varphi) The Attempt at a Solution I think its just a sphere with a radius of 2 _______________________________________________ Homework Statement Graph the solid whose given coordinates...
  17. O

    Z coordinate of the center of gravity

    Hey, for this problem i need to find the z coordinate of the center of gravity. I have a cylinder/disk whose height is along the y-axis and radiates about the x and z axis. what is the equation to find z bar. this is just one part of the problem.
  18. R

    Solving for Spherical Coordinate Angles in 3D: Understanding the Formulas

    Hi guys, This is my first time in this forum, thanks for your time. Now, I learn about spherical angles (vektor) in 3 Dimension I still confuse about the formula, such as: Fx = F sinφ cosθ ( in X axis = i) Fy = F sinφ sinθ ( in y-axis = j) Fz = F cosφ ( in z axis = k) I...
  19. K

    Vectors and 3D Coordinate Geometry

    Homework Statement Suppose that II c R3 is a plane, and that P is a point not on II. Assume that Q is a point in II whose distance to P is minimal; in other words, the distance from P to Q is less than or equal to the distance from P to any other point in II. Show that the vector PQ is...
  20. stevebd1

    Time coordinate in the rain frame

    I'm currently looking at Metric for the Rain Frame in 'Exploring Black Holes' by Taylor & Wheeler (page B-13) and while it's straightforward understanding drrain (which basically equals dr), I'm having a problem getting my head around dtrain. The following is a step-by-step approach but for some...
  21. I

    How Do You Solve Challenging Polar Coordinate Problems?

    HELP! I just got this assignment over the email a couple hours ago and it's due in the morning and I have no clue how to do these problems! I've spent a few hours trying to figure this stuff out on my own, but I'm down to these last few and I just can't do it. if you can answer one or more, I...
  22. S

    Find Unit Vector Orthogonal to a & b - Help Needed

    hi! I'm new to the forums, and had a question that was more calculus-related than physics. i saw another post similar to this one, but it was incomplete and i couldn't get the answer with the information on it, any chance someone could help me out? The question is: "Find a unit vector with a...
  23. R

    Vector angle in a standard x-y coordinate system?

    A certain vector has x and y components that are equal in magnitude. Which of the following is a possible angle for this vector in a standard x-y coordinate system? 30° 180° 90° 60° 45° Is this problem too simple or am i missing something? if the x and y components are equal in...
  24. F

    Parabolic coordinate system question

    Homework Statement a 3D solid is bounded by 2 paraboloids. The binding condition in cartesian coordinates is -1+(x2+y2) < 2z < 1-(x2+y2) a) rewrite the binding condition in parabolic coordinates b) using parabolic coordinates and the (already derived) metric tensor, find the volume of...
  25. F

    Coordinate space and momentum space

    Homework Statement given A(k)=N/(k2+a2) calculate psi(x) and show that (delta k * delta x) > 1 independent of the choice of a The Attempt at a Solution I calculated psi(x) to be (N*pi/a)*e-|ax| Would it be ok to compute <x> and <x2> in coordinate space and <k> and <k2> in...
  26. V

    Convert a cylindrical coordinate vector to cartesian coordinates

    Homework Statement Convert the following cylindrical coordinate vector to a Cartesian vector: \overrightarrow{A}\,=\,\rho\,z\,sin\,\phi\,\hat{\rho}\,+\,3\,\rho\,cos\,\phi\,\hat{\phi}\,+\,\rho\,cos\,\phi\,sin\,\phi\,\hat{z} Homework Equations...
  27. C

    In coordinate geometry does x=o mean the y axis or the yz plane ?

    In coordinate geometry does x=o mean the y-axis or the yz plane!? ? ?
  28. H

    Conversion Between Coordinate Systems

    Hello, I've been stuck on this problem for awhile and I've tried googling up some solutions but I still cannot find an answer to this question. Homework Statement An x-y coordinate system is shown below. A second system, u-v, is also shown. What is the relationship between the u-coordinate...
  29. DrGreg

    Accelerated coordinate systems

    This is in response to the following in another thread: I answer it here to avoid diverting that other thread's course. I'm assuming that Fredrik refers to using the plane of simultaneity of the co-moving inertial observer as a means of assigning coordinates to events in an accelerating...
  30. G

    Question about cylindrical (ie. 3d polar) coordinate system.

    Question Details: Convert the following equation into cylindrical coordinates... x^2 + y^2 + z^2 = 4 It's obvious that r^2 = x^2+y^2... but that would only simplify the equation to: r^2 + z^2 = 4 ... is there a better way to do this?
  31. A

    Coordinate transformation and choice of a suitable coordinate system.

    Consider the line element: ds^2=-f(x)dt^2+g(x)dx^2 in a coordinate system (t,x) where f(x) and g(x) are two functions to be determined by solving Einstein equation. But I can always make a transformation g(x)dx^2=dy^2 and then calculate everything in the (t,y) coordinate system. My...
  32. A

    Uniform circular motion and coordinate system

    2. In the figure below the particle P is in uniform circular motion. The motion is centered on the origin of an xy coordinate system. (a) At what values of \vartheta is the vertical component r_{y} of the position vector greatest in magnitude? (b) At what values of \vartheta is the...
  33. E

    A question of protein subunit symmetry and normal coordinate analysis

    Hey Im doing vibrational spectroscopy (Raman, nir, vis/uv) of a protein called C-reactive Protein. Its a symmetric molecule regarding the subunits http://en.wikipedia.org/wiki/C-reactive_protein Then i wondered if one can apply normal coordinate analysis (using symmetry and group theory) to...
  34. stevebd1

    Gravity and coordinate acceleration

    I'm looking to establish a simple explanation of coordinate acceleration- Basically, as GR established, gravity is the curvature of space. If we use the ball on a trampoline analogy (which is a 2 dimensional representation of what is happening in 3 dimensions), we have a sphere creating a...
  35. P

    Unitary coordinate transformation = rotation?

    Homework Statement Suppose I define a linear coordinate transformation that I can describe with a matrix U. If U is unitary. i.e. U^{-1}U = UU^{-1}=1 does that necessarily imply that the transformation corresponds to a pure rotation (plus maybe a translation), so that I may assume that...
  36. C

    Proving the Linear Independence of Coordinate Curves on a Smooth Surface

    I'm stuck on a problem on vector calculus. Given a surface S defined as the end point of the vector: \mathbf{r}(u,v) = u\mathbf{i} + v\mathbf{j} + f(u,v)\mathbf{k} and any curve on the surface represented by \mathbf{r}(\lambda) = \mathbf{r}(u(\lambda),v(\lambda)) and it mentions the...
  37. P

    Converting between coordinate systems?

    Homework Statement I have a bit of a general question, and I don't know whether or not the problem has a solution, but here's the idea behind it. I have two coordinate systems, let's call them CS A, and CS B. I have an infinite set of corresponding points for each system (both are 3D, so I...
  38. F

    Coordinate Rotation in a Cartesian 3-Space

    I have been trying to derive a set of equations for a new Cartesian coordinate system after a rotation of an original coordinate system. This is what I did: 1) I transformed the Cartesian coordinates (x,y,z) into spherical coordinates (r,p,q): x= r cos(q) cos(p) y= r cos(q) sin(p)...
  39. S

    Distance between two points in polar coordinate system.

    Guys, Any ideas on how to calculate distance between two points in Polar coordinate system without converting their coordinates to Cartesian? Ps. I know that if I converted from Polar (r, t) to Cartesian (x, y) by x = r.cos(t), y = r.sin(t), then the distance between two points would be d =...
  40. F

    Does Every Coordinate System Admit Local Othornormal Basis Vectors

    I wonder if there are coordinate systems that gobally curve and twist and turn and curl, that do NOT admit local orthonormal basis. I know that the Gram-Schmidt procedure converts ANY set of linear independent vectors into an orthnormal set that can be used as local basis vectors. And I assume...
  41. J

    How Do You Determine the Limits for r and θ in a Cylindrical Coordinate System?

    What are the r and θ limits for the triple integral of y where there's a parabloid cylinder x=y^2 and planes x+z=1 and z=0? I rearranged x+z=1 to get z=1-x => so 1-rcosθ; 0 ≤ z ≤ 1-rcosθ but I don't know how to get the limits for θ or r. How do I do this?
  42. DrGreg

    What Defines a Null Coordinate in Spacetime Metrics?

    Coordinates are sometimes described as "null coordinates". An example in SR is the coordinate u = x - ct. Another example is one of the coordinates in the Eddington-Finkelstein metric. But I've never seen an explicit rigorous definition of a null coordinate. The defining property seems to be...
  43. Y

    Integrating a Spherical Coordinate Problem

    Homework Statement Evaluate the integral below, where H is the solid hemisphere x^2 + y^2 + z^2 ≤ 9, z ≤ 0 \iiint 8-x^2-y^2\,dx\,dy\,dz. Homework Equations none The Attempt at a Solution \int_{0}^{2\pi} \int_{\frac{\pi}{2}}^{\pi} \int_{0}^{3} (8-2p^2 \sin^2{\phi}) p^2...
  44. S

    Mass on a spring question - coordinate system?

    Greetings, Regarding a mass on a spring – I know the classic differential equation is m \frac {dx^2(t)}{dt^2} + B \frac {dx(t)}{dt} + kx = f(t) F(t) = outside force applied B = damping coefficient “X” is in the vertical direction and +x direction is down. In reading I have...
  45. K

    Lorentz invariance and General Coordinate transformations

    Sorry to bring up again a question that I asked before but I am still confused about this. In SR we have Lorentz invariance. Now we go to GR and one says that the theory is invariant under general coordinate transformations (GCTs). But, as far as I understand, this is simply stating that...
  46. P

    Coordinate system for specifying the precise location of objects in space?

    Homework Statement which of the following is a coordinate system for specifying the precise location of objects in space? a. frame of reference b. diagram c. x-axis d. y-axis Homework Equations The Attempt at a Solution I thought it would be a diagram since it would use vectors...
  47. K

    General Coordinate transfos vs Lorentz transfos in GR

    GR is invariant under general coordinate transformations. If I understand correctly, this is basically devoid of any physical content. It just means that relabelling points does not change anything physical. So it's devoid fo physical content, right? On the other hand, in special...
  48. T

    Coordinate acceleration without a Force

    Coordinate acceleration without a Force ! Hi GR had presented two types of motion , the geodesic motion and the non-geodesic motion . We know that the geodesic motion equation is : \[ \frac{{d^2 x^\alpha }}{{d\tau ^2 }} + \Gamma _{\beta \mu }^\alpha \frac{{dx^\beta }}{{d\tau...
  49. H

    The z coordinate of the center of mass of the box

    Homework Statement A cubical box has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length L = 97 cm. Find (a) the x coordinate, (b) the y coordinate, and (c) the z coordinate of the center of mass of the box. Homework Equations...
  50. E

    Right-handed coordinate systems

    Homework Statement Everyone tells me that I should use right-handed coordinate systems. But no one tells me what happens if I don't. What is the danger of not using right-handed coordinate systems?Homework Equations The Attempt at a Solution
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