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. R

    Calculating Position and Angle of a Particle on a 2D Plane

    "Simple" Coordinate Problem Homework Statement The following happens on a 2D X-Y Plane. A particle accelerates at {3t m/s2}i + 4t m/s2}j where t = seconds At t = 0, the position of the particle is {20.0 m}i + {40.0m}j At t = 0, the velocity of the particle is {5.00 m/s}i + {2.00 m/s}j At...
  2. M

    How Is Collision Speed Calculated in a Supermarket Parking Lot Incident?

    Homework Statement On a supermarket parking lot, a car is pulling out and bumping into an oncoming car. The car pulls out with 0.8 m/s, while the oncoming car has a speed of 1.2 m/s. The angle between the velocities is 24 degrees, as indicated in the figure. What is the collision speed...
  3. S

    Transformations Between Coordinate Systems

    Homework Statement The velocity of a ball in an x-y coordinate system is (10, -5) where distance is measured in metres. A second coordinate system, p-q, uses units of feet (1 ft = 0.3048 m). The p-axis is oriented at alpha = 15 degrees relative to the x-axis. The origin of the p-q system is...
  4. D

    What is galileian system of coordinate?

    What is Galileian system of coordinate? I have read the chapter about it by einstein but still can't understand it. Can anyone kindly explain it to me? thanks
  5. T

    Two in-phase loudspeakers on a coordinate plane

    Homework Statement Two in-phase loudspeakers are located at (x, y) coordinates (-3.0, +2.0) and (-3.0, -2.0) . They emit identical sound waves with a 2.0 m wavelength and amplitude a. Determine the amplitude of the sound at the five positions on the y-axis (x=0): with y=0.0 with y=0.5 with...
  6. M

    Coordinate transformation under rotation

    If a system is rotated around Z axis then the new coordinates are X'= xcos() - Y sin(), Y'= Xsin() + Ycos() Z'= Z How is this obtained ?? () --->theta , angle of rotation around Z axis .
  7. L

    How Do You Convert Between Two Coordinate Systems with Different Basis Vectors?

    Homework Statement 2 coordinate systems are given: 1st: \vec{a}, \vec{b}, \vec{c} 2nd: \vec{m}, \vec{n}, \vec{p} in system \vec{a}, \vec{b}, \vec{c} basis vectors of 2nd system have values: \vec{m}=\{2/3, 1/3, 1/3\}, \vec{n}=\{-1/3, 1/3, 1/3\}, \vec{p}=\{-1/3, -2/3, 1/3\} also known that...
  8. T

    16 different spherical coordinate systems

    I've tabulated 16 possible ways of creating different spherical coord systems, and attached an image below to demonstrate them all. They are all spheres, though the coordinate system is different for each one. Assume an orthographic projection. Some are blanked out, since they are similar to...
  9. L

    Length of curve in Polar coordinate system

    I want to caculate length of curve in Polar coordinate system like this: if r=r(a) then length of the curve is ∫r(a)da Is this right? if not ,why ? What's the right one ? I konw the way in rectangular coordinate system,I just want to do it in Polar coordinate system .
  10. R

    Vectors and coordinate transformations

    Can anyone explain why it's important to be able to take vectors in an x,y,z coordinate system and be able to transform them into other coordinate systems. Could not all vector considerations be grappled with in the standard x,y,z coordinate systems? How important is this ability to physicists...
  11. 9

    Need help on this coordinate geomeotry question

    So here's how it goes. Find the coordinates of the centre and the radius of the circle x^2 + y^2 - 4x + 6y -12 =0 a)If the circle cuts the x-axis at the points A and B , find the length of line segment AB. My question is , I have actually found 2 points , they are (-2,0) and (6,0)...
  12. I

    Proving the Change of Coordinate Matrix for Left-Multiplication Transformation

    Homework Statement Prove: Let A \in \mathrm{M}_{n \times n}(\mathbb{F}) and let \gamma be an ordered basis for \mathbb{F}^n . Then [\boldmath{L}_A]_{\gamma} = Q^{-1}AQ , where Q is the nxn matrix whose jth column is the jth vector of \gamma . Homework Equations \boldmath{L}_A...
  13. F

    Looking for a good webpage with different coordinate systesms

    Anyone have a good link to a site explaining the different coordinate systems and the jacobian determinant for each of them. Thanks EDIT: I actually just need a website wiht a list of the different transformations ie. polar: x = u*cos(v) y = u*sin(v) v \in [0,2\pi], u \in [0,radius] J = r
  14. M

    How can I convert coordinates from Spherical to Cartesian?

    I do not understand Spherical coordinate system. I'm asked to compare the differences with Cartesian coordinate but I have no idea how to start. So I would like some help that will at least give me a understanding of the spherical coordinate system, thx
  15. P

    Normal coordinate substitutions with periodic boundary conditions

    Could someone plase hep me with normal coordinate substitutions with periodic boundary conditions, I can't see where the 1/N cancels in the attached file Thanks Doug
  16. J

    Vector Coordinate Conversion & Phasors

    I would attempt to solve these questions with "relevant equations", but my questions simply derive from an attempt of understanding class notes. If someone could attempt to help my understanding, that would be great. I've attached the PDF file that contains my corresponding questions...
  17. M

    Transformation of Coordinate Systems

    Homework Statement Find a one-to-one C1 mapping f from the first quadrant of the xy-plane to the first quadrant of the uv-plane such that the region where x^2 \leq y \leq 2x^2 and 1 \leq xy \leq 3 is mapped to a rectangle. Compute the Jacobian det Df and the inverse mapping f^{-1}. The...
  18. B

    Does coordinate system = gauge ?

    Does "coordinate system" = "gauge"? Are "coordinate system" and "gauge" the same thing? What about "coordinate transformation" and "gauge transformation"?
  19. H

    Del Operator for Cylindrical Coordinate

    http://img208.imageshack.us/img208/5153/12802868.png Why is the del operator for cylindrical coordinate the upper one and not the lower one? How does the 1/r term arises?
  20. A

    Geometry in spherical coordinate

    Hi all: I am wondering if there is any book or course note about the geometry in spherical coordinate. Not just the superficial definition and the convertion with Euclidean coordinate. But something like how a line is defined in spherical coordinate in 3D space, how a plane is defined, how to...
  21. Z

    Evaluate the iterated intergal by converting to polar coordinate?

    Help me Evaluate the iterated intergal by converting to polar coordinate: http://www.ziddu.com/gallery/4894419/Untitled.jpg.html
  22. B

    What are the Limits for Computing the Volume of a Cylinder Inside a Sphere?

    Hi Guys, I have been given the coordinates of a cylinder inside a sphere and want to convert to Cylindrical coordinates to compute the volume of the cylinder. Can you please check the limits and integral I have? The cylinder is x^2+y^2= 4 sphere = x^2+y^2+z^2= 9 As its a cylinder...
  23. D

    What is the significance of covariance in general relativity?

    Any relationship between mass, length and time in general relativity can be considered using tensors of Einstein's Field Equations which are independent of the coordinate system used and of the origin of that coordinate system Is there a formal name for such coordinate independence and origin...
  24. M

    Finding AREA in POLAR COORDINATE

    Homework Statement Find the area inside one leaf of the four-leaved rose r = cos2xHomework Equations A = 1/2 antiderivative abr2 dxThe Attempt at a Solution I just need help in finding the lower and upper limits of integration. But besides that, I know how to do the rest. If my integration is...
  25. M

    Coordinate transformation of nabla operator

    Hi all! I am studying the Galilean group of transformations and I'm not sure how to transform the Nabla operator. Consider the 2 transformations: (x,t)->(x+s,t) (x,t)->(Dx,t) and the expression "nabla (x)" where D is a matrix and x, s are vectors I am pretty sure that I have...
  26. R

    Mathematica - Colour each 2D point by a third coordinate for each point?

    I'm looking, as an observer, at imaging accretion discs and tori around Kerr black holes. The image of the disc/torus is projected onto a 2D grid (a CCD if you like) so all lensing effects etc. are implicit. Basically, I can plot the image after determining the (x,y) coordinates in the 2D grid...
  27. T

    Coordinate transformation of contravariant vectors.

    Note: The derivatives are partial. I've seen the coordinate transformation equation for contravariant vectors given as follows, V'a=(dX'a/dXb)Vb What I don't get is the need for two indices a and b. Wouldn't it be adequate to just write the equation as follows? V'a=(dX'a/dXa)Va...
  28. J

    Change of Coordinate Matrix

    In geometry the change of variable, x = (2 / sqrt(5))x' - (1 / sqrt(5))y' (#1) y = (1 / sqrt(5))x' + (2 / sqrt(5))y' (#2) can be used to transform the equation 2x^2 - 4xy + 5y^2 = 1 into the simpler equation (x')^2 + 6(y')^2 = 1, in which form it is easily seen to be the...
  29. J

    Vector calc question - coordinate systems

    Homework Statement How do you derive the divergence in cylindrical coordinates by transforming the expression for divergence in cartestian coordinates? Homework Equations F = F_x i + F_y j + F_z k div F = ∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z (divergence in Cartesian coordinates) I need to transform...
  30. J

    Coordinate systems for divergence

    Homework Statement Compute the divergence in cylindrical coordinates by transforming the expression for divergence in cartestian coordinates. Homework Equations F = F_x i + F_y j + F_z k div F = ∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z ... (divergence in cartesian coordinates) I need to...
  31. R

    Center of Krunskl Szekeres coordinate

    Why is the spacetime flat at the center of the krunskal szekeres coordinates?
  32. F

    Coordinate Transformation - velocity?

    If I have a velocity vector V in some coordinate system. Is there anything special that needs to be done to convert V -> V' ? Basically, I have a matrix (N x 3) in north-east-down coordinates. I am trying to convert (a row at a time_ to another matrix (N x 3) to earth-centered-earth-fixed...
  33. H

    Taking foureir integral in polar coordinate

    hi; I have a question about taking the foureir trasnform in polar coordinate... the question is as following; https://www.physicsforums.com/attachment.php?attachmentid=17892&stc=1&d=1236524155 I would like to learn that according to outermost integral (\rho), the integral is taken. But...
  34. L

    Verifying Orthogonal Curvilinear Coordinate System

    For the transformation u_1=2x-y u_2=x+2y u_3=3z verify that the u_i form an orthogonal curvilinear coordinate system
  35. A

    4D angular coordinate system and corresponding hypervolume element

    I am looking for a 4D angular coordinate system (radius and three angles) and its corresponding "hypervolume element". 2D: polar coordinates - dA = r dr dtheta 3D: spherical coordinates - dV = r^2 sin(phi) dphi dtheta dr 4D: ?
  36. W

    Change of Coordinate for V.Field in Mfld.

    Hi, again: Just a quick question; I have "notation indigestion", i.e., I have been trying to figure way too many technicalities recently; I would appreciate a quick yes/no: Say X_p is a V.Field defined at p in a C^k manifold; k>0 . Say (U,Phi) and (U',Phi') are...
  37. Ed Aboud

    Coordinate geometry of the circle question

    Homework Statement Fairly straight forward question but I just can't see what's wrong. A circle passes through the point (2,-4) and touches both the x-axis and the y-axis. Find the equations of the two circles which satisfy these conditions. Homework Equations x^2 + y^2 + 2gx + 2fy...
  38. Jonathan Scott

    Extrapolating Schwarzschild exterior coordinate

    As is well known, the relationship between the Schwarzschild radial coordinate (defined by the proper area of a spherical surface) and the proper distance in the radial direction is very different for the exterior and interior solutions. This makes it difficult to visualize what happens if we...
  39. A

    Electric field from potential and coordinate

    Homework Statement I am given V(x,y,z) = 3x^2 + 2y + 5 and I am given s = (5,3,1), so what is the electric field? Homework Equations V= Es The Attempt at a Solution I really have no idea. What I tried: Derivative of V(x,y,z) = 6x+2 so E = 32 N/C? Really I just don't...
  40. R

    Y coordinate of the system's center of mass?

    Homework Statement In Fig. 9-39, three uniform thin rods, each of length L = 28 cm, form an inverted U. The vertical rods each have a mass of 12 g; the horizontal rod has a mass of 31 g. What are (a) the x coordinate and (b) the y coordinate of the system's center of mass? (Give your answer in...
  41. R

    Coordinate Geometry(Right Triangle)

    Homework Statement If y=x+2, y=2x+3 are medians of right angled triangle ABC (angle A=90) through B and C respectively such that |BC|=81 units. Find area of triangle. The Attempt at a Solution I have been trying this since a long time. I am posting my work in the form of 2 images. I hope my...
  42. P

    Coordinate change in de Sitter spacetime

    Hello folks. Just registered, first post (moved here from the Physics forum). Let there be a de Sitter metric in static coordinates: ds^2 = - [1 - (r/R)^2] c^2 dt^2 + dr^2 / [1 - (r/R)^2] + r^2 d(omega)^2 where: r is the radial coordinate R is the cosmological horizon...
  43. M

    Curl of a vector in a NON-orthogonal curvilinear coordinate system

    Hi, I have a certain NON-orthogonal curvilinear coordinate system in 3D (in the metric only g_{13}=g_{23}=g_{31}=g_{32}=0) and I want to take the curl (\nabla\times\mathbf{v}) of a vector. Any idea on how to do this? The only information I can find is about taking the curl of a vector in...
  44. D

    Coordinate Transformation (and using line elements)

    This is from Hartle's GR book, in one of the first chapters it talks about diff geom, nothing too advanced, but I am learning on my own. Homework Statement It's part E I have trouble with. Read e. and skip to last para if you want. Consider this coordinate transformation: x=uv ...
  45. C

    X and x' in two coordinate relativistic systems

    let's say we have two coordinate systems ( S-OXYZ and S'-O'X'Y'Z') , S' moving with velocity v away from S . At t=0 O=O'. According to Lorentz' transformations we have : At t=0 x in as a function of x' : x=\frac{x'}{\sqrt{1-\beta^2}}=x'\gamma Now, say I know x(I just found it above) ...
  46. C

    Vector components in Polar Coordinate

    Hi! In a non-uniform circular motion if I have two components of a vector in cartesian coordinates then how to find the tangential and radial components of a vector. For example ; I have Vx and Vy as horizontal and vertical components of a vector V respectively. Vx and Vy can lie in all...
  47. pellman

    Time as coordinate in many-body relativistic mechanics

    In pre-relativistic mechanics a system of N particles would be described by 3N coordinates x_i,y_i,z_i parametrized by time t. Would a relativistic system be properly described by 4N coordinates x_i,y_i,z_i,t_i, with a time variable for each particle? If so, how can we ever speak of the...
  48. D

    Achieving normal derivative in spheroidal coordinate

    Homework Statement Hi PhysicsForums, I am calculating something related to the spheroidal membrane and want to ask you a question. I consider a oblate spheroid (Oblate spheroidal coordinates can also be considered as a limiting case of ellipsoidal coordinates in which the two largest...
  49. D

    Normal derivative in spheroidal coordinate

    Hi PhysicsForums, I am calculating something related to the spheroidal membrane and want to ask you a question. I consider a oblate spheroid (Oblate spheroidal coordinates can also be considered as a limiting case of ellipsoidal coordinates in which the two largest semi-axes are equal in...
  50. A

    Cartesian coordinate space transformation question

    I have a question that I am trying to find proof and/or references for: Suppose we have two sets of points (P1 and P2) in separate N-dimensional Cartesian Spaces S1 and S2. *** Note: if it can be easily extended to the Euclidean Space - even better. We need to find Affine Transformation...
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