What is Coordinates: Definition and 1000 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. D

    Triple integral in spherical coordinates

    Homework Statement The problem is to calculate the volume of the region contained within a sphere and outside a cone in spherical coordinates. Sphere: x2+y2+z2=16 Cone: z=4-√(x2+y2) Homework Equations I am having difficulty converting the equation of the cone into spherical coordinates...
  2. P

    Laplacian in Spherical Coordinates

    Homework Statement Homework Equations All above. The Attempt at a Solution Tried the first few, couldn't get them to work. Any ideas, hopefully for each step?
  3. C

    Log transform on cylindrical coordinates

    Homework Statement I'd like to do a log transform on the radius variable of the heat conservation equation: qr - qr + Δr= ΔE/Δt where qr= -kA(dT/dr) My solution for this equation in cylindrical coordinates is: Tt+Δt=Tt+(Δt*k)/(ρ*c*Δr^2)* [(Tt-1-Tt)/(ln(rt/rt-1) - (Tt-Tt+1)/(ln(rt+1/rt)]...
  4. K

    Help with a triple integral in spherical coordinates

    Homework Statement Use spherical coordinates. Evaluate\int\int\int_{E}(x^{2}+y^{2}) dV where E lies between the spheres x2 + y2 + z2 = 9 and x2 + y2 + z2 = 25. The attempt at a solution I think my problem may be with my boundaries. From the given equations, I work them out to be...
  5. B

    Scalar product in spherical coordinates

    Hello! I seem to have a problem with spherical coordinates (they don't like me sadly) and I will try to explain it here. I need to calculate a scalar product of two vectors \vec{x},\vec{y} from real 3d Euclidean space. If we make the standard coordinate change to spherical coordinates we can...
  6. H

    Cannot finish calculating a double integral with change of coordinates

    Homework Statement Integrate: \displaystyle f\left( x,y \right)=\frac{{{x}^{2}}}{{{x}^{2}}+{{y}^{2}}} on the region: \displaystyle D=\left\{ \left( x,y \right)\in {{\mathbb{R}}^{2}}:0\le x\le 1,{{x}^{2}}\le y\le 2-{{x}^{2}} \right\} TIP: Use change of coordinates: \displaystyle...
  7. 3

    What is the triple integral of z^2(x^2 + y^2) over a bounded cylindrical region?

    Homework Statement Let W= {(x,y,z)| x^2 + y^2 ≤ 1, -1 ≤ z ≤ 1} (W is a bounded cylindrical region) Evaluate the triple integral f(x,y,z)= z^2 x^2 + z^2 y^2 over W. Use cylindrical coordinates Homework Equations i don't see any relevant equations besides the obvious cylindrical...
  8. M

    Physical Meaning of r in BL Coordinates

    Not much else to say other than the title. In the Schwarzschild spacetime, the radial coordinate r didn't represent radial distance, but it at least represented the thing that determines the area of a sphere centered on the large mass. It doesn't seem like that interpretation can be given to the...
  9. D

    MHB Boundary conditions spherical coordinates

    Laplace axisymmetric $u(a,\theta) = f(\theta)$ and $u(b,\theta) = 0$ where $a<\theta<b$. The general soln is $$ u(r,\theta) = \sum_{n=0}^{\infty}A_n r^n P_n(\cos\theta) + B_n\frac{1}{r^{n+1}}P_n(\cos\theta) $$ I am supposed to obtain $$ u(r,\theta) = \sum_{n =...
  10. A

    Shifting coordinates for mechanical problems

    More and more my teacher has talked about how results for mechanical problems are the same no matter what our coordinate system is (though it may be easier to calculate them in some coordinate frames). I must however admit, that I have never really had a clear explanation of what it means to do...
  11. N

    Going from cylindrical to cartesian coordinates

    Homework Statement Hi The expression for the magnetic field from an infinite wire is \boldsymbol B(r) = \frac{\mu_0I}{2\pi}\frac{1}{r} \hat\phi which points along \phi. I am trying to convert this into cartesian coordinates, and what I get is \boldsymbol B(x, y) =...
  12. F

    Finding 2D coordinates in different frames

    Hi guys, i need help for homework, it seems easy, but i can't do it:cry:, no calculation to do only writing 2D coordinates in different frames. Homework Statement The hallmark of an inertial frame is that any object which is subject to zero net force will travel in a straight line in a...
  13. U

    Number of points having integral coordinates

    Homework Statement Let A,B,C be three sets of complex numbers as defined below A = {z:|z+1|\leq2+Re(z)}, B = {z:|z-1|\geq1} and C=\left\{z: \frac{|z-1|}{|z+1|}\geq 1 \right\} The number of point(s) having integral coordinates in the region A \cap B \cap C is Homework Equations...
  14. W

    Finding coordinates of a point on a circle( angle and distance from O known)

    1. I basicly have to find the coordinates of P. All the pink lines are know, coordinates of points A and centre of circle are know. 2. (x-a)^2 + (y-b)^2 = r^2 [b]3. I try to substitute mx+c into the equation and get (x-a)^2 + (y-mx-c)^2 + r^2= 0 but I can't work out what m and c...
  15. G

    Velocity of flow in cylindrical coordinates

    An infinitely long cylindrical bucket with radius a is full of water and rotates with constant angular velocity \Omega about its horizontal axis. The gravity is in the vertical direction. The velocity of the flow in cylindrical coordinates (whose z axis is the horizontal axis of the bucket) is...
  16. B

    Using polar coordinates, show that lim (x,y)->(0,0) [sin(x^2+y^2)]/[x^2+y^2] = 1

    Homework Statement Using polar coordinates, show that lim (x,y)->(0,0) [sin(x^2+y^2)]/[x^2+y^2] = 1 Homework Equations r^2=x^2+y^2 The Attempt at a Solution I was able to get the limit into polar coordinates: lim r->0^+ [sin(r^2)]/r^2 but I'm not sure how to take this limit. I tried...
  17. M

    Dynamics Polar Coordinates question

    Hi everyone. I am a little desperated cause my exam is on monday and still much stuff to do. I don't get when I am supposed to use/consider radial and tranversal forces. Most excercises say "it rotates on the horizontal or vertical" I guess this is the info that tells me if there is...
  18. D

    MHB Laplace equation polar coordinates

    I have never solved an equation in polar form. I am not sure with how to start. Solve Laplace's equation on a circular disk of radius a subject to the piecewise boundary condition $$ u(a,\theta) = \begin{cases} 1, & \frac{\pi}{2} - \epsilon < \theta < \frac{\pi}{2} + \epsilon\\ 0, &...
  19. M

    Express the equation in rectangular coordinates

    Homework Statement An equation is given in spherical coordinates. Express the equation in rectangular coordinates. r2cos2∅=z So first thing I did was used a half angle formula r2 (cos2∅-sin2∅=z Now, I'm stuck. The answer is x2-y2=z Guidance is appreciated (: Homework...
  20. C

    Good resource on covariant/contravariant, magnetic coordinates, and jacobians?

    First post here in PF, so forgive me if this question is in the wrong place. I'm a student in computational plasma physics. The code I work with utilizes magnetic field aligned coordinates, and as a necessity, it is sometimes useful to convert between spatially regular coordinates (cartesian...
  21. N

    Determine x and y coordinates of resultant force through object

    Homework Statement The concrete slab supports the six vertical loads shown. Determine the x- and y-coordinates of the point on the slab through with the resultant of the loading system passes. Image attached Homework Equations The Attempt at a Solution I started off by...
  22. D

    Integration of a Circle in Polar Coordinates

    Homework Statement Hi, I'm trying to find the area of a circle in polar coordinates.I'm doing it this way because I have to put this into an excel sheet to have a matrix of areas of multiple circles. Here is an example of the problem. a= radius of small circle (gamma, r0) = polar coordinate...
  23. P

    Is There a Simple Explanation for the Area Element in Fermi Normal Coordinates?

    Hi everyone, Defined the Fermi Normal Coordinates (which can be seen for example http://relativity.livingreviews.org/open?pubNo=lrr-2011-7&amp;page=articlese10.html" ) is there any heuristic argument to explain why the area element is something proportional to the element of solid angle? I...
  24. J

    Help with Cartesian to Ellipsoidal Coordinates

    Homework Statement I need to isolate the expressions for ellipsoidal coordinates (see below)... I'm given: x2=\frac{(a^2+\lambda)(a^2+\mu)(a^2+\nu)}{(a^2-b^2)(a^2-c^2)} y2=\frac{(b^2+\lambda)(b^2+\mu)(b^2+\nu)}{(b^2-a^2)(b^2-c^2)}...
  25. B

    How do you calculate declination and Right Ascension from Earth Coordinates?

    Say a person is positioned here: 40.23°N and 15.89°E and was examining the night sky. How do you calculate the declination and Right Ascension from that location's coordinates? I know the RA is measured in hours up to 24 and Declination in degrees. Any ideas?
  26. D

    Area of a Circle in Polar Coordinates

    Hi, I'm trying to find the area of a segment of a circle that is not at the origin. It will look similar to this picture below but I need to find the area enclosed by a circle. Using the polar equation of a circle provided by wikipedia: and integrating to find the area of a...
  27. perplexabot

    Polar to rectangular coordinates

    Hello all. I am trying to change: E = (1/r) ar To rectangular coordinate system. Where ar is a unit vector. So I know r = √(x^2 + y^2) i also think ar = ax+ay, where ax and ay are unit vectors along the x-axis and y-axis respectively. So that would give me: E = (1/√(x^2 + y^2)) (ax...
  28. S

    Euler equation in Polar coordinates

    Hello. I have 2D Euler equation for fluids. I can't derive it in polar coordinates. I defined functions u(x,y,t) = u'(r, theta, t) and v(x,y,t) = v'(r, theta, t). I started by computing derivatives \frac{\partial u'}{\partial r}=\cos\theta\frac{\partial u}{\partial...
  29. J

    Angular momentum polar coordinates

    Homework Statement from the cartesian definition of angular momentum, derive the operator for the z component in polar coordinates L_z = -ih[x(d/dy) - y(d/dx)] to L_z = -ih(d/dθ) Homework Equations x = rcosθ y = rsinθ r^2 = x^2 + y^2 r = (x^2 + y^2)^1/2 The Attempt at...
  30. F

    Vectors and finding coordinates question

    Homework Statement On a treasure map, A = -5 (km)x + 2 (km)y, B = 4 km, and theta = 328 deg. The treasure is located at C = 4A - 3B. What is the x-coordinate of the treasure? What is the y-coordinate of the treasure? Homework Equations a^2 + b^2 = c^2 Vector addition The...
  31. S

    Hamiltonian in spherical coordinates

    Homework Statement The total energy may be given by the hamiltonian in terms of the coordinates and linear momenta in Cartesian coordinates (that is, the kinetic energy term is split into the familiar pi2/2m. When transformed to spherical coordinates, however, two terms are angular momentum...
  32. M

    Cylindrical coordinates

    From this equation x2 + y2 = 2y I was wondering how in the solutions manual it was decided that 0≤z≤1 ? Edit: Don't read... I was looking at a solution to a different problem
  33. S

    Conversion of energy expression from Cartesian to spherical coordinates

    A text I am reading displays the attached image. Can someone explain the general method for obtaining the velocity analogues of those terms (in parentheses) in 1.5? I know the second and third terms in parentheses in 1.6 and 1.7 are the squares of angular velocities, but can a general procedure...
  34. C

    Describe the surface in cylindrical coordinates?

    Homework Statement The surface is x^2/y*z=10. Put this into cylidrical coordinates. in the form r=f(theta,z) Homework Equations No clue The Attempt at a Solution No clue
  35. P

    How do i find acceleration and x/y coordinates given time and i/j values?

    Homework Statement At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of i = (3.00 i - 2.00 j) m/s and is at the origin. At t = 2.70 s, the particle's velocity is = (9.30 i + 6.90 j) m/s. (a) Find the acceleration of the particle at any time t. =...
  36. V

    Simple integral in cylindrical coordinates

    Homework Statement As a part of bigger HW problem, I need to calculate the integral: \oint[\hat{r}+\hat{z}]d\phi Homework Equations The Attempt at a Solution In cylindrical coordinates: =[\hat{r}+\hat{z}] \ointd\phi =2∏[\hat{r}+\hat{z}] On the other hand if I convert it to...
  37. M

    Finding Acceleration Given Coordinates

    No idea how to do this. An object moving with uniform acceleration has a velocity of 11.0 cm/s in the positive x-direction when its x-coordinate is 2.91 cm. If its x-coordinate 2.75 s later is −5.00 cm, what is its acceleration? The answer is -10.1 cm/s squared but I don't know how to get...
  38. T

    Derivation of Laplace Operator in Spherical and Cylindrical Coordinates

    Hey Guys, Does anyone know where I can find a derivation of the laplace operator in spherical and cylidrical coordinates?
  39. O

    Circumference of a circle (in strange coordinates)

    Homework Statement We are given a function defined by x = uv, y = 1/2 (u^2-v^2)Homework Equations I derived the line element ds^2 = (u^2+v^2) dv^2 + (u^2+v^2) du^2 However I decided this was to unwieldy to derive our circumference where C = 2*{R}\oint_{-R}^{R} ds So I decided to try to...
  40. T

    Cylindrical and Spherical Coordinates Changing

    Homework Statement Convert the following as indicated: 1. r = 3, θ = -π/6, φ = -1 to cylindrical 2. r = 3, θ = -π/6, φ = -1 to cartesian The Attempt at a Solution I just want to check if my answers are correct. 1. (2.52, -π/6, 1.62) 2. (-2.18, -1.26, 1.62)
  41. S

    Finding the curl in diffrent coordinates by transforming variables

    we have a well known and simple equation for curl in cartesian coo. now we want it in let's say cylindrical coordinates. question is...can we transform every thing to cylinderical and then use the formula for cartesian?I mean writing basis vectors of cartesian in terms of r and theta and z and...
  42. mnb96

    Is a change of coordinates a diffeomorphism?

    Hello, the definition of diffeomorphism is: a bijection f:M\rightarrow N between two manifolds, such that both f and f-1 are smooth. Is it thus correct to say that a (admissible) change of coordinates is a diffeomorphism between two manifolds?
  43. T

    Converting Polar to Cartesian Coordinates

    I was given the problem r=2sin(2(θ)). I'm supposed to write the equation in the Cartesian Coordinates. I understand the basics to this but I'm not really sure how I'm supposed to write the equation when I have x=2sin(2(θ))cos(θ) and y=2sin(2θ)sin(θ).
  44. R

    Spherical coordinates, vector field and dot product

    Homework Statement Show that the vector fields A = ar(sin2θ)/r2+2aθ(sinθ)/r2 and B = rcosθar+raθ are everywhere parallel to each other. Homework Equations \mathbf{A} \cdot \mathbf{B} = |\mathbf{A}||\mathbf{B}|\cos(0) The Attempt at a Solution So, if the dot product equals 1. They should be...
  45. A

    Transforme kinetic energy in parabolical cyndrical coordinates

    Homework Statement The transformation from cartesian coordinates to cylindrical coordinates is given by: x = 1/2 (u2 - v2), y=uv, z=z Homework Equations compute the kinetic energy 1/2mv2 in parabolic cylindrical coordinates The Attempt at a Solution Any ideas??
  46. Z

    Trouble understanding meaning of triple integral in spherical coordinates

    Homework Statement Evaluate \iiint\limits_B e^{x^2 + y^2 + z ^2}dV where B is the unit ball. Homework Equations See above. The Attempt at a Solution Does this evaluate the volume of f(x, y, z) within the unit ball (i.e. anything falling outside the unit ball is discarded)...
  47. A

    Expressing Spherical coordinates in terms of cylindrical

    Homework Statement I'm trying to express spherical coordinates in terms of cylindrical and vice versa. I would appreciate it if someone could give me some feedback on my attempt at a solution. Thanks for the help! The Attempt at a Solution Spherical(cylindrical) r=(ρ^2+z^2)^(1/2)...
  48. E

    Volume integral of an ellipsoid with spherical coordinates.

    Homework Statement By making two successive simple changes of variables, evaluate: I =\int\int\int x^{2} dxdydz inside the volume of the ellipsoid: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}}=R^{2} Homework Equations dxdydz=r^2 Sin(phi) dphi dtheta dr The...
  49. B

    Determining XY coordinates from quadrilateral measurements

    I'm trying to determine the XY coordinates of 3 corner points of a quadrilateral shape based on known lengths of the sides of that shape. I know the lengths of all 4 sides of the shape as well as the lengths of both cross lengths (effectively making two adjacent triangles). I've attached a...
  50. Vorde

    Trying to Understand Generalized Coordinates

    I am trying to understand what generalized coordinates are but I'm having some trouble. After reading up on them a bit my best understanding of the idea of generalized coordinates is the following: Because choice of coordinate system is arbitrary when solving physical systems (or anything for...
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