What is Coordinate: Definition and 909 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. A

    MHB Solving for U & P in a Coordinate Change

    Assume that you are given a coordinate change on a line which changes the coordinate x to a new coordinate z given by the formula z=U⋅x+P where U,P are real numbers with U non zero. If the new coordinate of the point -13 is 12 and the new coordinate of the point -7 is 6 then we must have U= ...
  2. 9

    Coordinate transformation - NED and ECEF frames

    Hi, I have a reference device that outputs euler angles, which are angles that relate the sensor body frame to the north east down frame. These angles are called pitch roll and yaw. The sensor is an accelerometer. I know how to get the rotation matrix that will put accelerations from the...
  3. A

    Finding the coordinate of a point by Law of Cosines/Sines

    Homework Statement A model for the suspension of a vehicle is shown where the spring has stiffness k = 178 N.mm and an unstretched length of 347 mm. Here is the picture: http://i.imgur.com/1dTVs12.jpg Part a asked to determine the value of P and the force supported by member AB so that the...
  4. B

    Is There a Simpler Way to Express Hyperbolic Coordinates in Terms of x and y?

    This system of coordinates: can be "translated" in terms of x and y, so: x = \sqrt{\frac{\sqrt{u^2+v^2}+u}{2}} y = \sqrt{\frac{\sqrt{u^2+v^2}-u}{2}} Exist another form more simplified of write x and y in terms of u and v? I tried rewrite these expressions using the fórmulas of half angle but...
  5. yango_17

    Sketching solids given spherical coordinate inequalities

    Homework Statement Sketch the solid whose spherical coordinates (ρ, φ, θ): 0≤ρ≤1, 0≤φ≤(pi/2) Homework EquationsThe Attempt at a Solution I was thinking that since ρ represented the distance from the point of the origin and φ represented the angle between the positive z-axis and the ray through...
  6. davidbenari

    How coordinate lines transform under ##e^z=\frac{a-w}{a+w}##

    Homework Statement Say how coordinate lines of the z plane transform when applied the following transformation ##e^z=\frac{a-w}{a+w}## Homework EquationsThe Attempt at a Solution This is exactly the way the problem is stated. It is a pretty weird transformation in my opinion and I'm guessing...
  7. Math Amateur

    MHB Elementary Algebraic Geometry: Dummit & Foote Ch.15, Ex.24 Coordinate Ring

    I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need help to get...
  8. Math Amateur

    MHB Elementary Algebraic Geometry: Exercise 23, Sect 15.1 Dummit & Foote

    I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need help to get...
  9. Math Amateur

    MHB Coordinate ring of an affine algebraic set - k[A^n]/I(V)

    I am trying to gain an understanding of the basics of elementary algebraic geometry and am reading Dummit and Foote Chapter 15: Commutative Rings and Algebraic Geometry ... At present I am focused on Section 15.1 Noetherian Rings and Affine Algebraic Sets ... ... I need someone to help me...
  10. applestrudle

    I Example of *Non* Cartesian Vector/Tensor (not the coordinate s

    ...system, I mean as in the Cartesian Vector/Tensor definition. I get that if you have two mutually orthogonal basises which are theta degrees apart and the transformation from one basis to the other follows the same as a rotation by theta degrees i.e: V'i = Rij Vj then it is a Cartesian...
  11. Anukriti C.

    Why Is the Slope Between Perpendicular Lines -1, But Not for the X and Y Axes?

    we know that in the cartesian plane, slope between two perpendicular lines is -1. but what about the x and y axis? if we find the slope between them it is not equal to -1. why is the slope between two perpendicular lines on the cartesian plane is -1 but the axes themselves do not behave such?
  12. newjerseyrunner

    Coordinate translation on a rotating plane

    I have this problem where I need to convert from mouse coordinates on the screen with relative coordinates on an object that can be arbitrarily translated, scaled, and rotated around another arbitrary position. I've already normalized all of the units to be the same (pixels) but the trig is...
  13. P

    Electric force-finding coordinate

    Homework Statement The y-axis marks the boundary between the area where the is no electric field (in the second and third quadrant) and the area where there is a constant electric field: E = 610j N/C (in the first and fourth quadrant). An electron travels along the negative x-axis toward the...
  14. E

    Linear Transformation and isomorphisms

    Homework Statement Suppose a linear transformation T: [P][/2]→[R][/3] is defined by T(1+x)= (1,3,1), T(1-x)= (-1,1,1) and T(1-[x][/2])=(-1,2,0) a) use the given values of T and linearity properties to find T(1), T(x) and T([x][/2]) b) Find the matrix representation of T (relative to standard...
  15. E

    Bases and Coordinates: B1 and B2 for [R][/3] - Homework Statement

    Homework Statement Let B1={([u][/1]),([u][/2]),([u][/3])}={(1,1,1),(0,2,-1),(1,0,2)} and B2={([v][/1]),([v][/2]),([v][/3])}={(1,0,1),(1,-1,2),(0,2,1)} a) Show that B1 is a basis for [R][/3] b) Find the coordinates of w=(2,3,1) relative to B1 c)Given that B2 is a basis for [R[/3], find...
  16. Priyadarshini

    How Do You Tell When A Compound Will Form A Coordinate Bond?

    How can you tell when a compound will form a covalent bond or a coordinate bond? I know that a coordinate bond is a special type of covalent bond and if during covalent bonding, if the elements taking part do not obtain a noble gas configuration, they for coordinate bonds. But take for example...
  17. Luca_Mantani

    Doubt regarding volume element in Spherical Coordinate

    Homework Statement Hi everyone. Here's my problem. I know that the volume element in spherical coordinate is ##dV=r^2\sin{\theta}drd\theta d\phi##. The problem is that when i have to compute an integral, sometimes is useful to write it like this: $$r^2d(-\cos{\theta})dr d\phi$$ because...
  18. D

    How Do Coordinate Transformations Work Between Different Systems?

    Homework Statement Transform the coordinates from the red c-system to the blue system. (Picture) Homework Equations Using(X Y) for the red cartesian system and (x y) for the blue system The Attempt at a Solution The solution to this problem gives x=Xcos▼ + Ysin▼ y=-Xsin▼+Ycos▼ Im not sure...
  19. A

    Area in polar coordinate using multiple integral

    The question is to find the area of a disk, r ≤ 2a×cos(θ) as in the figure "example-just an illustration" I used two methods, each gave different wrong answers - integrate 2a×cos(θ) dθ dr - from θ=0 to θ=π/2 and from r=2a to r=2a×cos(θ) ; then I simply multiplied the answer by 2. - integrate...
  20. S

    Orthogonality of a curvilinear coordinate system

    Homework Statement Show that the uvw-system is orthogonal. r, \theta, \varphi are spherical coordinates. $$u=r(1-\cos\theta)$$ $$v=r(1+\cos\theta)$$ $$w=\varphi$$ The Attempt at a Solution So basically I want to show that the scalar products between \frac{\partial \vec{r}}{\partial u}...
  21. shanepitts

    What type of coordinate system?

    This is a very basic question, but what type of coordinate system is this? When is it useful to use? er, eθ, eΦ sinθ
  22. K

    Point rotating in a coordinate system

    The point P rotates with angle α to point P'. the coordinates of the old P are x1 and x2 and for P': x'1 and x'2. Prove that: $$x'_1=x_1\cos\alpha+x_2\sin\alpha$$ $$x'_2=x_2\cos\alpha-x_1\cos\alpha$$ I drew on the left the problem and on the right my attempt. the line OA, which is made of...
  23. TrickyDicky

    Coordinate conditions in cosmology

    The FRW cosmology is a solution of the FRW that can be foliated into 3D isotropic and homogeneous slices. This foliation is implemented mathematically first by the use of a not generally covariant coordinate condition https://en.wikipedia.org/wiki/Coordinate_conditions#Synchronous_coordinates ...
  24. C

    3D Coordinate transformation and Euler Angles

    Hello, I'm running a galaxy formation simulation. The output specifies the coordinates in (x, y, z) of all the particles in a galaxy, which usually fall in a disk. The orientation of the disk depends on the initial conditions, but it is generally not aligned with any of the coordinate axes...
  25. D

    Local parameterizations and coordinate charts

    I have recently had a lengthy discussion on this forum about coordinate charts which has started to clear up some issues in my understanding of manifolds. I have since been reading a few sets of notes (in particular referring to John Lee's "Introduction to Smooth Manifolds") and several of them...
  26. R

    Magnetic Field in Spherical Coordinate

    Homework Statement I am trying to use the equation ##B_{dip} (r) = \nabla \times A## to find the magnetic field due to a dipole at the origin pointing in the z direction (where A is the magnetic vector potential). The correct answer should be: ##B_{dip} (r) = \frac{\mu_0 m}{4 \pi r^3} \ (2...
  27. stevendaryl

    Question about Coordinate Change

    Suppose that I have a two-dimensional coordinate system (x,y) and I change to a new coordinate system (u,v). What I know is that there is some function \theta(u,v) such that: \dfrac{\partial x}{\partial u} = cos(\theta) \dfrac{\partial x}{\partial v} = -sin(\theta) \dfrac{\partial y}{\partial...
  28. E

    Time derivative of 3D Spherical Coordinate

    When we obtain the velocity vector for position vector (r, θ, φ) Why do we take the time derivative of the radial part in the 3D Spherical Coordinate system only? Don't we need to consider the polar angle and azimuthal angle part like (dr/dt, dθ/dt, dφ/dt)?
  29. D

    Coordinate charts and change of basis

    So I know that this involves using the chain rule, but is the following attempt at a proof correct. Let M be an n-dimensional manifold and let (U,\phi) and (V,\psi) be two overlapping coordinate charts (i.e. U\cap V\neq\emptyset), with U,V\subset M, covering a neighbourhood of p\in M, such that...
  30. Andre' Quanta

    Distinction between coordinate and reference frame

    How is it possible to distinguish a change of coordinate from a change o reference frame? I had this problem while i was studying Rindler' s coordinates: is it only another way to describe a Minkowsky space-time region or does it rappresent a region of the space time as described by an...
  31. K

    The speed of a curve in different coordinate systems

    Hello, If for a curve in Cartesian coordinates ##||\dot{{\mathbf r}}||=\mbox{const}## (i.e. the curve is constant speed) will the speed of the curve change in cylindrical and spherical coordinates? Could someone experienced share how the transition from flat Euclidian space to curved space...
  32. Breo

    Why to change from momentum space integrals to spherical coordinate ones?

    So I was asked to compute loop contributions to the Higgs and compute the integrals in spherical coordinates, I gave a look to Halzen book but did not found anything. Why, when and how to make that change?
  33. F

    Transition and coordinate matrices

    Homework Statement Consider the bases B = {b1,b2} and B' = {b'1,b'2} for R2, where b1=(1, -1), b2=(2,0), and b'1=(1,2), b'2=(1,-3) a. Find the transition matrix P from B to B' b. Compute the coordinate matrix [p]B, where p=(4,3); then use the transition matrix P to compute [p]B' Homework...
  34. Adoniram

    How to write this state vector in coordinate basis?

    Homework Statement I am given this state, which is the result of a lamba particle decaying into a proton and neutral pion. Initial j = 3/2. The final state can theoretically be written as: I have already determined that: alpha_p = Sqrt[2/3] beta_p = Sqrt[1/3] alpha_d = -/+ Sqrt[2/5]...
  35. K

    2D Maxwell complex coordinate stretching PML

    Hello, I'm trying to derive the perfectly matched layer for the TM mode Maxwell's equations using a complex coordinate stretching. As seen in http://math.mit.edu/~stevenj/18.369/pml.pdf . But I'm running in a bit of trouble somehow. \partial_t H_x =-\mu^{-1} \partial_y E_z\\ \partial_t H_y...
  36. AdityaDev

    Equation of family of circles

    In my textbook, its given that the equation of family of circles touching a given circle S and line L is ##S+\lambda L=0## So to find the equation of family of circles touching line L at point P(p,q), can i use the same equation taking S to be a circle of radius zero and center at P? That is...
  37. T

    Difference between frame of reference and coordinate system?

    Homework Statement Our teacher said we can NEVER do an F=ma problem from an accelerating, or noninertial frame. (He said there are ways to do it, but we can not do it in his class), and I'm confused becuase often times he makes the "system" or makes a "free-body diagram" around an accelerating...
  38. ognik

    Orthogonal coordinate systems - scale factors

    Homework Statement Start from the 'relevant equation' below and derive $$ (1) \frac{\partial{\bf{\hat{q}}_{i}}}{{\partial{q}}_{j}}={\hat{q}}_{i}\frac{1}{{h}_{i}} \frac{\partial{h}_{i}}{{\partial{q}}_{j}}, {i}\ne{j}$$ $$ (2) \frac{\partial{\bf{\hat{q}}_{i}}}{{\partial{q}}_{i}}= -\sum...
  39. brianeyes88677

    Magnetic force in a moving coordinate system

    Consider a line charge with charge density λ and a electric charge q. A coordinate system moving at velocity v ,it will see the line charge as a current ,and the electric charge(which is also moving seen from the moving coordinate system) will feels magnetic force. Why does this happens?
  40. N

    Deciphering a coordinate system in an XML file

    Hello, firstly I have to make the usual apologies of ignorance and inexperience, but that's why I'm here! I have a library of XML files which each contain two sets of image data. Together they make something very similar to this:http://imgur.com/vjs7MRH The grey and red points are given in...
  41. J

    What are momentum,configuration and coordinate spaces?

    What is a momentum space,a coordinate space and a configuration space? Are they in classical or quantum mechanics or both? What are their similarities and differences and when,where and how are they used? thank you in advance!
  42. binbagsss

    How to classify coordinate as S-L,Null,T-L?

    I'm looking at the extension of the Schwarzschild metric using Kruskal coordinates defined as ##u'=(\frac{r}{2M}-1)^{\frac{1}{2}e^{\frac{(r+t)}{4M}}} ## ##v'=(\frac{r}{2M}-1)^{\frac{1}{2}e^{\frac{(r-t)}{4M}}} ## In these coordinates the metric is given by...
  43. binbagsss

    Schwarzschild Extension Coordinate Transformation Algebra

    So I have the metric as ##ds^{2}=-(1-\frac{2m}{r})dt^{2}+(1-\frac{2m}{r})^{-1}dr^{2}+r^{2}d\Omega^{2}##* I have transformed to coordinate system ##u,r,\phi, \theta ##, where ##u=t-r*##(2), where ##r*=r+2m In(\frac{r}{2m}-1)## and to the coordinate system ##v,r,\phi, \theta ##, where...
  44. B

    Normal-Tangential Coordinate for Ball Moving in Circle

    Homework Statement The problem is: The ball B is traveling on a horizontal circle table. It is attached to the string that leads through a hole in the center of the circle. At the very beginning, the ball B is traveling around a circular path counter-clockwise, then the cord is pulled down...
  45. K

    Hi can you help me in solving this from coordinate geometry?

    < Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > Find the equation of a line passing through point A (1, 2) and whose perpendicular distance from origin is maximum.
  46. X

    Inclined plane normal force varies by coordinate system?

    Suppose we have a block on an inclined plane. If we choose the x-y axis to be parallel and perpendicular to the inclined plane, then we have Fy = N - mgcos30 = 0 But if we choose our trivial x-y coordinate system, where y is parallel to the force of gravity, then we get: Fy = Ncos30 - mg =...
  47. onethatyawns

    Trigonometry just the conversion factor of coordinate types?

    I think trig is assumed to be based upon triangles. This lumps trig next to squares, trapezoids, pentagons, hexagons, etc. Sure, triangles can be used to describe trig functions, but I think they do a disservice to your intuition. It's similar to Riemann sums versus integrals. True, integrals...
  48. Ibix

    Coordinate basis for cotangent space

    Warning: this may be totally trivial, or totally wrong. I've been working through Sean Carroll's lecture notes, and I've got to http://preposterousuniverse.com/grnotes/grnotes-two.pdf . I follow the derivation for showing that the tangent space bases are the partial derivatives (Carroll's...
  49. Calpalned

    Intersection of a circle with coordinate planes

    Homework Statement Find an equation of the sphere with center (2, -6, 4) and radius 5. Describe its intersection with the each of the coordinate planes. Homework Equations Equation of a sphere with three dimensions X2 + Y2 + Z2 = R2 The Attempt at a Solution My equation is (x - 2)2 + (y +...
  50. D

    Vectors in Tangent Space to a Manifold Independent of Coordinate Chart

    In Nakahara's book, "Geometry, Topology and Physics" he states that it is, by construction, clear from the definition of a vector as a differential operator [itex] X[\itex] acting on some function [itex]f:M\rightarrow\mathbb{R}[\itex] at a point [itex]p\in M[\itex] (where [itex]M[\itex] is an...
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