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

    Convert tensor from cartesian to cylindrical coordinate

    Homework Statement Given the tensor F_{\mu \nu }= \left[ \begin{array}{cccc} 0 & -E_{x} & -E_{y} & -E_{z} \\ E_{x} & 0 & B_{z} &-B_{y} \\E_{y} & -B_{z} & 0 & B_{x} \\E_{z} & B_{y} & -B_{x} & 0 \end{array} \right] F^{\mu \nu }F_{\mu \nu }=2(B^2-\frac{E^2}{c^2}) and metric tensor n_{\mu \nu...
  2. J

    Proof of one of the properties of Real Coordinate Vector Spaces

    1. Homework Statement Prove that there is an additive identity 0∈R^n: For all v∈R^n, v+0=v2. Homework Equations Axiom of Real Numbers: There is an additive identity 0∈R : For all a∈R, a+0=a and o+a=a 3. The Attempt at a Solution Solution 1 (My own attempt) : Let v=(v1, v2, v3... vn). Then...
  3. H

    Coordinate System of Coupled Oscillators and 4D Phase Space representation

    Coordinate System of Coupled Oscillators and "4D" Phase Space representation So, I've modeled the interaction between two cantilever beams with the kinetic and potential energies shown in the above figure. The cantilevers are very stiff and have a small oscillation amplitude, so they can be...
  4. A

    How to get the new Coordinate of an Polygon at angle X

    Let say I have a triangle(polygon). I know all the co-ordinates of all points(x1,x2,x3,y1,y2,y3). Let say the polygon is inclined(at x3,y3) and it's angle is 30 degree. How to get the point x4, y4?
  5. E

    Is the Radial/Transverse coordinate system a non-inertial reference frame ?

    Hey guys, I am having some problems with the concept of inertial/non-inertial frames of reference and their applications in engineering dynamics. So I've learned that a given frame of reference is defined to be non-inertial when something in the studied system can only be explained through...
  6. A

    Drawing curves in Spherical coordinate

    I had a tutorial today and my tutor said these questions are very trivial so we can simply look at it at home. But after going home, I found that I don't know how to do Q 35. I know that p<3 is responsible for the big sphere with r=3. But I don't know why the other part is responsible for...
  7. B

    How do you find the coordinate of a vector with the unit vector?

    If you already have one of the two coordinates?
  8. G

    Question about relating basis of curvilinear coordinate systems.

    Wikipedia gives the relationship between a cartesian and curvlinear coordinate system as gi=(partial)x1/(partial)zi +(partial)x2/(partial)zi http://en.wikipedia.org/wiki/Curvilinear_coordinates Where gi is the i'th basis in the curvlinear coordinate system, x1 and x2 are the cartesian...
  9. N

    Coordinate and proper time animation

    Someone posted this animation in a previous discussion and I just 'rediscovered' it in my notes: http://www.adamtoons.de/physics/gravitation.swf Do you experts think it accurate, and if so, wouldn't this be a nice tool to display coordinate time versus proper time?? [Is it worth...
  10. W

    Time as Parameter in QM vs Coordinate in QFT

    According to Peterdonis in an old thread According to Matterwave in https://www.physicsforums.com/showthread.php?t=573589 msg #11: Peterdonis said Time is a parameter in non-relativistic QM while as a coordinate in relativistic QM/QFT. But Matterwave said parameter and coordinate has...
  11. M

    Coordinate time and proper time.

    Hello, So, I have just started studying relativity, and I am confused about some basic concepts in relativity. So, the book we use says that that time has three different kinds, proper or path time, coordinate time and spacetime intervals. I understand that coordinate time is the same as...
  12. M

    Coordinate based vs non-coordinate based differential geometry

    Hello Everyone, I am just wondering what the difference in these is. Could someone please give a brief example of non-coordinate based differential geometry vs the equivalent in coordinate based, or explain the difference (whichever is easier)? Also, what advantages does one have over the...
  13. B

    Why Does Rotating Coordinate Axes Affect Calculations?

    Homework Statement 17. xy = 2 The Attempt at a Solution Do you see that step where they do the following: √2/2 - √2/2 = my answer is 0 and they multiply that to √2/2 + √2/2 = my answer is √2 So to me the answer is 0 * √2 = 0, but the book shows that that calculation = 2, then they...
  14. D

    Understanding Negative t Coordinates in Lorentz Transformations

    In lorentz transformation, why has t -sign
  15. V

    Solving for Euler angles and 3-D coordinate Rotations.

    Hi, (attachment with visuals is included) I have a 3-D vector dataset that is measured in a reference frame (measurement reference frame) that is oriented relative to a horizontal coordinate system. In this dataset I have x-y- and z-component data for the vectors relative to a coordinate...
  16. B

    Coordinate Space Transformations

    Hi, I hope this is the right forum to post. My question is, which is the math implied for transforming an objectA local space, to anothers objects local space, and then transforming it to world space? For example, Lets say we want to know if objectA is infront of objectB, So the...
  17. J

    Cylindrical Coordinate System. Please check my answer

    Homework Statement (a) In cylindrical coordinates , show that \hat{r} points along the x-axis is \phi = 0 . (b) In what direction is \hat{\phi} if \phi = 90° Homework Equations The Attempt at a Solution here is my solution. for a. \vec{r} = \rho cos \phi \hat{i} + \rho...
  18. J

    What is necessary to memorize for coordinate systems?

    I've been told that for upper level physics classes it's imperative to know how to switch between coordinate systems, however I'm unsure of what is exactly necessary to know. For example, today I was reading up on divergence and I noticed that there are formulas for divergence in spherical and...
  19. C

    What does the time coordinate represent in spacetime?

    Hello PF, I have just been given an introduction to special relativity and its postulates. One of the consequences of special relativity of course is that space and time are entangled and that in order to assign a coordinate to an event, you must give it spatial (x, y ,z) and temporal...
  20. M

    Prove: QR Passes Through O If PQ, PR on xy=c2 Inclined Equally

    Homework Statement Given that P,Q and R lie on the hyperbola xy=c2, prove that if PQ and PR inclined equally to the coordinate axes, then QR passes through O. Homework Equations The Attempt at a Solution I don't understand what does ''PQ and PR are inclined equally to the...
  21. R

    Spherical Coordinate Systems(Cartesian, i think it called)

    Me and my friend have been arguing about the coordinate system used for the earth... specifically gravity. he's trying to tell me the value of gravity is -9.8ms/2, when I've read from several books and other online resources that's it 9.8ms/2... a positive number. Hes keeps going on and on and...
  22. M

    Find 4th Tangent for 2 Circles Coordinate Geometry

    Homework Statement 2 circles have the equation x2+y2-2x-2y+1=0 and x2+y2-12x-12y+36=0 respectively. Both circle touches the x-axis, y-axis and the line 3x + 4y = 12. Find the fourth tangent of the 2 circles. Homework Equations The Attempt at a Solution This is second part of the...
  23. M

    Coordinate Geometry: Finding the Locus of a Midpoint on a Curve

    Homework Statement A variable point P lies on the curve y2 = x3 and is joined to a fixed point A with coordinate (2,0). Prove that the locus of the mid-point of AP is y2= 2(x-1)3. Homework Equations The Attempt at a Solution According to what i know, I need to know the...
  24. A

    Forces and defining coordinate systems

    Homework Statement Homework Equations F=ma vi=vf + at The Attempt at a Solution If i was to define upward as positive y direction, would the answer be = -881 pounds (btw why is the answer in the image in Newtons?) and because i defined upward as +y would ƩF = T - w? where w = mg.
  25. C

    Prove coordinate vectors are unique for given basis

    Homework Statement Prove that the coordinates of a vector v in a vector space Vn are unique with respect to a given basis B={b1,b2,...,bn} Homework Equations The Attempt at a Solution not sure at all what to do with this
  26. M

    Solving Cylindrical Coordinate Equation with $\delta$ Functions

    Homework Statement Solve in cylindrical coordinates -m\delta(z)\delta(\rho-a)=\partial^2_z A(z,\rho)+\partial^2_\rho A(z,\rho)+\frac{1}{\rho}\partial_\rho A(z,\rho)-\frac{1}{\rho^2}A(z,\rho) Where \partial_i is the partial derivative with respect to i. Homework Equations It is...
  27. S

    Integration - Find the x coordinate and the area under the curve

    Homework Statement http://imageshack.us/photo/my-images/703/dfdfu.jpg Homework Equations To find the x coordinate 1. Make both equations equal, expose e and take logs. I'm not sure how to do this and I've tried but keep getting the wrong answer. 2. To find the area, subract the...
  28. Ranger Mike

    CNC Coordinate Measurement Machine Controller

    Question - Regarding a cnc cmm controller, What is tunneling? How is this measured? What impact does the cmm structure have on this characteristic?
  29. H

    Combination of cartesian and cylindrical coordinate system

    Hi, I have to solve a numerical problem namely how air is flowing first through a porous medium followed by streaming of the air coming out of the porous medium in a very narrow channel flowing to the ambient (journal porous air bearing). This problem can be described with the use of two...
  30. S

    Find the x coordinate of the stationary point of the following curves

    Homework Statement Find dy/dx and determine the exact x coordinate of the stationary point for: (a) y=(4x^2+1)^5 (b) y=x^2/lnx Homework Equations The Attempt at a Solution (a) y=(4x^2+1)^5 dy/dx=40x(4x^2+1)^4 40x(4x^2+1)^4=0 Find x... How? (b) y=x^2/lnx...
  31. C

    Coordinate transform of partial derivative

    Homework Statement How does ∂aAb behave under coordinate transformations in special relativity? Work out ∂'aA'b Homework Equations The Attempt at a Solution I have been given back the solution sheet to this problem, but I don't understand it. This is what I have I get...
  32. D

    Polar coordinate to compute the volume

    Homework Statement Use polar coordinates to compute the volume of the region defined by 4 - x^{2} - y^{2} ≤ z ≤ 10 - 4x^{2} - 4y^{2} Homework Equations The Attempt at a Solution I got z = 2 so set up the equation V = f^{2pi}_{0}f^{5/2}_{2}f^{0}_{2}r*dzdrdθ is the domain...
  33. D

    Domain for Polar Coordinate Part 2

    Homework Statement f(x,y) = e^{x^2+y^2} x^{2} + y^{2} ≤ R Homework Equations The Attempt at a Solution I believe this is a circle. f^{2pi}_{0}^{sqrt(R)}_{-sqrt(R)}e^{x^2+y^2}*r*dr*dθ = f^{2pi}_{0}f^{sqrt(R)}_{-sqrt(R)}e^{r^2}*r*dr*dθ after u substitution... =...
  34. D

    Defining the Domain for a Polar Coordinate Function

    Homework Statement f(x,y) = y(x^{2} + y^{2})^-1 y ≥ \frac{1}{2}, x^{2} + y^{2} ≤ 1Homework Equations The Attempt at a Solution Would you check my domain please? f^{pi}_{0}f^{sqrt(3)/2}_{-sqrt(3)/2} sinθ drdθ
  35. D

    Integration in Polar - polar coordinate

    Homework Statement f(x,y) = xy x ≥ 0, y ≥ 0, x^{2} + y^{2} ≤ 4 Homework Equations The Attempt at a Solution f^{pi/2}_{0}f^{2secθ}_{0} rcosθ * rsinθ * r drdθ I just wanted to check... is this right?? because I really don't think it is
  36. R

    How to convert velocity potential from polar form to Cartesian coordinate form

    Homework Statement Alright, here's the question, A stream function for a plane, irrotational, polar-coordinate flow is ψ=9r^2sin^θ. Find out the velocity potential in Cartesian Co-ordinate! Homework Equations The Attempt at a Solution Well, I can easily find out the velocity...
  37. C

    Coordinate change to remove asymptotic geodesic?

    Through my mathematical fumblings, I think I have found a metric which gives a solution of the geodesic equation of motion that is asymptotic. It is a diagonal metric, with g00 = (x_1)^(-3) and g11 = 1. I am largely self-taught with SR so I may be miles off, but I think this gives a G.E. of M...
  38. E

    Coordinate systems - finding optimal? simple conceptual question

    today in my physics course we were using jacobians to transform coordinate systems. This made me wonder if there was a way of deriving an optimal coordinate system to use for a given problem. -optimal meaning most simplified equation of a surface or bounds of a constraint (ex. cylindrical...
  39. O

    Switch the divergence coordinate system

    Homework Statement i have the divergence in the (x,y,z) Cartesian as \frac{dA_x}{dx}+\frac{dA_y}{dy}+\frac{dA_z}{dz} and the assignment is to transfer it to cylindrical system (r,{\phi},z), by any way i choose. Homework Equations tried with the chain rule, but i am doing...
  40. X

    Cartesian and Polar coordinate system increments

    we know that for any (x, y) in Cartesian system, there is such (r, θ) in Polar system, so x = r * cosθ and y = r * sinθ how you can calculate what corresponds to (Δx, Δy) in polar system? how come Δx * Δy = r * Δr * Δθ? Maybe this is very stupid question and has obvious answer...
  41. M

    Coordinate axis (which one is correct)?

    In the problem the book the book chose to use the axis in the left diagram... but why can you not use the coordinate axis from the right diagram?
  42. A

    Div and curl operators in a left-handed coordinate system?

    In a right-handed cartesian coordinate system the divergence and curl operators are respectively: \nabla \cdot A= \frac{\partial A_{x}}{\partial x}+\frac{\partial A_{y}}{\partial y}+\frac{\partial A_{z}}{\partial z} \nabla \times \mathbf{A}= \begin{vmatrix} \widehat{x} & \widehat{y} &...
  43. mnb96

    Curvilinear coordinate systems and periodic coordinates

    curvilinear coordinate systems and "periodic" coordinates Hello, we can consider a generic system of curvilinear coordinates in the 2d plane: \rho = \rho(x,y) \tau = \tau(x,y) Sometimes, it can happen that one of the coordinates, say \tau, represents an angle, and so it is "periodic"...
  44. M

    Why are the coordinate axis different for block M1 and M2 in this scenario?

    I am confused how they picked the direction right of block M1 to be -x and the downward direction of block M2 to be +x..? I didn't know that one could create two different coordinate axis. Correct me if I am wrong but it seems that if you are working with two diff body's that are not in...
  45. F

    Help with coordinate transformations

    Homework Statement I'm having trouble understanding coordinate transformations for vector fields. There are two 'coordinate pieces', the coordinates pieces of the vector at a point changes, and the function describing the field can also be rewritten in terms of the new coordinates. I'm...
  46. S

    Quick spherical coordinate question

    So I have the following shape for which I want to calculate the inertia matrix. Basically I just want to know what limits of integration I should use if I am using spherical coordinates. Assume the convention that phi is the angle from x to y in the xy plane and theta is from z to the xy plane...
  47. J

    It says convert (-1, pi/8 ) from polar to rectangular coordinate?

    How do you find these on the unit circle: 5pi/2 ? howabout pi/8 ? Converting from polar to rectangular? It says convert (-1, pi/8 ) from polar to rectangular coordinate? But there is no pi/8 on the unit circle? If the'yre on the unit circle just use x=rcosθ and y=rcosθ another example is for...
  48. P

    Calculate curvature by coordinate component method

    I'm trying to follow the math in Wald's General Relativity where he starts out with the equation for covariant derivative: \nablab\omegac = \partialb\omegac - \Gammadbc\omegad He uses that to derive the equation for a double covariant derivative: \nablaa\nablab\omegac =...
  49. S

    At what times does the object intersect one of the coordinate planes?

    Homework Statement r(t)={sin(pi*t),ln(t),((1/4)e^t} At what time(s) does the object intersect one of the coordinate axes? At what time(s) does the object intersect one of the coordinate planes? During what times t is the object in the first octant? Homework Equations Not...
  50. L

    Combining Coordinate Systems?

    While not paying attention in class my friend made a joke that a cube squared was in six dimensions, or something like that. Terrible joke, but now I'm trying to figure out if it is valid to arithmatically combine the basis vectors for two or more coordinate systems to get a new one.
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