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. A

    What Is the Particle's Speed When Its X Coordinate Reaches 15m?

    Homework Statement At t=0, a particle leaves the origin with the velocity of 9.0m/s in the positive y direction and moves in the xy plane with a constant acceleration of ( 2.0i-4.0j) m/s ^2 . At the instant the x coordinate of the particle is 15 m , what is the speed of the particle ...
  2. B

    Struggling to understand vecot coordinate mapping.

    I am somewhat puzzled after reading that polynomials can be vectors, this concept confuses me. For instance, they can say that a basis for polynomials P_2 can be. B=\{1+t^{2},t+t^{2},1+2t+t^{2}\} In this case will the mapping [1+t^{2}]_{B} be [1,0,0] or [1,0,1]?
  3. O

    Why must be that for curl vector in spherical coordinate?

    The correct one is 2nd, but why not first? Please guide , or tell me any link that relate to this derivation. Thanks
  4. E

    A cylinder rotating in Cartesian coordinate system

    Homework Statement In Cartesian coordinaate system, we describe the rotation of a cylinder. The axis of the cylinder has the same direction as the basis vector e3. Angular velocity is described by vector w = 2e1 - 5e2 + 7e3 rad/s. I must find the velocity vector (v) of a point P that is...
  5. N

    Express a vector in a rotated coordinate system

    Homework Statement Hi I have a coordinate system (x', y') and a vector v'=(1, 0) here. There is a different coordinate system (x, y), which is rotated about the y-axis relative to (x', y') by an angle Ω. I am trying to express v' in the system (x, y). At first what I tried to do was to...
  6. O

    Mechanics~polar coordinate & radial and transverse component

    http://www.answers.com/topic/radial-and-transverse-components From the above link, 1) e θ is a unit vector perpendicular to r in the direction of increasing θ. Where is the direction of increasing θ? Is that a circle? θ Increase from 0 to 2∏.then eθ moves in a circle? direction always...
  7. T

    Defining geometry within a cartesian coordinate system

    Hello, Just as a warning before anyone reads my question I am not a mathematician, just an engineer with moderate math skills he wants to expand. So I'm writing some engineering software which involves defining/interation/modification of geometry within a cartesian system but I currently...
  8. haael

    Transforming coordinate system into a rotating one

    I want to solve a following problem. Imagine a collection of massive points. Each point has mass, position, velocity, moment of inertia, orientation and spin. We can calculate its total center of mass, total momentum and total angular momentum. The task is to transform the coordinate system...
  9. B

    Orthogonal Coordinate Systems

    Hey guys, I'd really love it if you could post little essays explaining your intuition on how to derive the x, y & z coordinates from all/any of the orthogonal coordinate systems in this list, how you think about, say, bipolar coordinates if you had to re-derive the coordinate system on a desert...
  10. C

    Line element under coordinate transformation to get polar form

    Homework Statement Hello Guys, I am reading Hobson's General Relativity and I have come across an exercise problem, part of which frustrates me: 3.20 (P. 91) In the 2-space with line element ds^2=\frac{dr^{2}+r^{2}d\theta^{2}}{r^{2}-a^{2}}-\frac{r^{2}dr^{2}}{{(r^{2}-a^{2})}^{2}} and...
  11. M

    Schwarzchild radial coordinate

    The Schwarzschild spacetime can be foliated by 2-sphere, which are spacelike hypersurfaces of constant t and r (Schwarzschild coordinates) with a normal vector ##\partial_t## (outside the horizon). Because a 2-sphere has no center, the coordinate r is not the radius of the sphere and we consider...
  12. C

    Reference frames, reference particles, coordinate systems and all that

    Previously, before getting into relativity, I've always thought of a 'reference frame' of basically an "observer carrying a coordinate system" - where I thought of an observer as anything which could record information of positions and velocities of particles etc. Now, however, I'm reading a...
  13. O

    !Understanding Partial Derivatives of Coordinate Transformation

    Hi Everyone, I was studying coordinate transformation and I came across this equation, that I couldn't understand how it came up. Let me put it this way: x = rcosθ Then if I want to express the partial derivative (of any thing) with respect to x, what would be the expression? i.e. ∂/∂x=...
  14. ash64449

    Relation between coordinate time and proper time

    Hello friends, If we consider ##{T}## as coordinate time and ##{\tau}## as proper time, the relationship between them is: ##\frac{T}{\tau}= \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}## so, ##{T}= \frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}}## So we can consider this expression like this: If In...
  15. E

    How to determine all points of intersection in a polar coordinate

    Is there a way to find all points of intersection in a polar co ordinate graph without the need to draw the graph. i/e USing algebra? If so, how?
  16. A

    Apparent weight / Rotating coordinate system

    Homework Statement Show that, owing to the rotation of the Earth on its axis, the apparent weight of an object of mass m at latitude λ is : m((g-ω^{2}Rcos^{2}λ)^{2}-(ω^{2}Rcosλsinλ)^{2})^{1/2} where ω is the angular velocity of the Earth and R its radius. The first space travellers to reach...
  17. topsquark

    MHB Coordinate transformation derivatives

    I've had to hit my books to help someone else. Ugh. Say we have the coordinate transformation \bf{x}' = \bf{x} + \epsilon \bf{q}, where \epsilon is constant. (And small if you like.) Then obviously d \bf{x}' = d \bf{x} + \epsilon d \bf{q}. How do we find \frac{d}{d \bf{x}'}? I'm missing...
  18. H

    Mastering Coordinate Planes: Finding the Closest Plane to a Sphere's Center

    1. Determine which of the three coordinate planes is closest to the center of the sphere(or indicate which planes are tied if two or more of the distances are the same) (s-7)^2+(y-7)^2+(z-7)^2=36 Homework Equations 3. Would i just try setting x,y,z in turns equal to 0 to find...
  19. C

    Double integral new coordinate system calculation

    Homework Statement This is a 2 part question. I'm fine with the first part but the 2nd part I'm struggling with. The first part asks us to calculate the double integral, \int\intDx2dA for, D = {(x,y)|0≤ x ≤1, x≤ y ≤1} For this part I got an answer of 1/4. For the 2nd part we introduce a new...
  20. V

    Orthonormal basis vectors for polar coordinate system

    Firstly; is there a difference between the "regular" polar coordinates that use \theta and r to describe a point (the one where the point (\sqrt{2}, \frac{\pi}{4}) equals (1, 1) in rectangular coordinates) and the ones that use the orthonormal basis vectors \hat{e}_r and...
  21. G

    How can I rotate a coordinate system and write functions in the rotated system?

    Hey So, I was wondering how to convert from one coordinate axes to another... in particular, where the new axes are y = x and y = -x, as seen by the picture below I want it so that the Red dot in the new coordinate system will be (\sqrt2,0). Is there an easy way to do this? (My lookings on...
  22. ShayanJ

    Vectors in curvilinear coordinate systems

    To specify a vector in cartesian coordinate systems,we assume its tail to be at the origin and give the cartesian coordinates of its head.What about other coordinate systems? For example,in spherical coordinates,is the following correct? a \hat{x}+b \hat{y}+c \hat{z}=\sqrt{a^2+b^2+c^2}...
  23. T

    Polar coordinate integration in different planes?

    I know that when you are integrated over dA in the xy plane, for your polar coordinates, x = rcosθ and y = rsinθ. However what about in the xz and yz plane? I noticed in one of the textbook problems, where the integration is over an area in the xz plane, x = rcosθ and z = rsinθ. How did the...
  24. P

    Angle on coordinate axis, related acute angle

    Homework Statement Tan A = -2/6 a) Draw two possible locations on the coordinate axis for the terminal arm of angle A b) Find two possible values for the measure of angle A and the related acute angle. Homework Equations c^2 = a^2 + b^2 SOHCAHTOA The Attempt at a Solution I know...
  25. R

    What are Thermodynamic Coordinates and Why are Heat and Work Not Included?

    i don't really understand which quantities are thermodinamic coordinates and which are not. and what makes work and heat are not thermodinamic coordinates but temperature, volume, etc are thermodinamic coordinates?
  26. C

    MHB Polar coordinate components

    I'm stuck on the second part of this question. Suppose a particle moves in a plane with its trajectory given by the polar equation $r=2b\sin(\theta)$ for some constant $b>0$. (i) Show that this can be written in Cartesian coordinates as $x^2+(y-b)^2=b^2$. This is the equation for a circle of...
  27. C

    Understanding Coordinate Basis in Wald's GR

    In Wald's GR he makes use of a coordinate basis consisting of ∂/∂x^{n} where n runs over the coordinates, and I understand his argument that ∂f/∂x^{n} are tangent vectors, but I can't wrap my head around the operator ∂/x^{n} spanning a tangent space of a manifold. Any clarification on this would...
  28. J

    Coordinate patches on curved manifolds

    Dear All, I've been studying differential geometry for some time, but there is one thing I keep failing to understand. Perhaps you can help out (I think the question is quite simple): Can I use Cartesian coordinates to cover a curved manifold? I.e., is there an atlas that only contains...
  29. R

    The Earth Analemma and Orthonormal Coordinate Systems

    Hi. I have been researching the Earth-Sun analemma and I found this document about deriving the Earth-Sun analemma via orthonormal coordinate systems. Unfortunately I do not know very much about orthonormal coordinate systems and while I understand the first bit about elliptical angles, I...
  30. J

    Compressible flow in cylindrical coordinate

    Hi, could anyone tell me a reference on Navier-Stokes equation for the COMPRESSIBLE flow in CYLINDRICAL coordinate? Just can't find a good reference book. Thanks in advance. Jo
  31. S

    What Constitutes something being coordinate free

    What Constitutes something being "coordinate free" People say that exterior calculus ie. differentiating and integrating differential forms, can be done without a metric, in without specifying a certain coordinate system. I don't really get what qualifies something to be 'coordinate free', I...
  32. H

    Invariance of the y coordinate for a boost along the x axis

    Homework Statement I've been reading through Spacetime Physics by Taylor & Wheeler, but this argument about the invariance of the y coordinate for inertial frames, one moving relative to the other on the x axis, is tripping me up. I'll just write the text word for word: I'm just not...
  33. T

    Number of unknowns - Coordinate Transforms

    In general relativity, what are the total number of unknowns for a generic coordinate transform? Is it just 4 * 4 = 16? Is there a way to break those down into combinations of types, such as boosts, rotations, reflections (parity?), etc, or is it just left wide open from an interpretive...
  34. micromass

    The Elements of Coordinate Geometry by Loney

    Author: H.M. Schey Title: Div, Grad, Curl, and All That: An Informal Text on Vector Calculus Amazon Link: https://www.amazon.com/dp/0393925161/?tag=pfamazon01-20 Prerequisities: Calculus 1,2,3 Table of Contents: Preface Introduction, Vector Functions, and Electrostatics Introduction...
  35. N

    [Ma4b2] Isomerism in coordinate complexes cofusion

    Consider a complex with Central Metal atom M A and B are monodentate ligands . Consider a compound with formula as [M A4 B2] . Textbook and the web says there can be only 2 possible isomers of this compound . What I say is, why can't I in the first image put A on the top and bring B...
  36. D

    Find the angle of a triangle and x coordinate

    I have this triangle and I know just the two sides indicated there. How can I find angle theta? I tried decomposing the triangle in two right triangles and using trigonometry find one side, but I can't figure how to do that using just the hypotenuse
  37. F

    Is there a coordinate independent Dirac delta function?

    I have been wondering exactly how one would express the Dirac delta in arbitrary spaces with curvature. And that leads me to ask if the Dirac delta function has a coordinate independent expression. Is there an intrinsic definition of a Dirac delta function free of coordinates and metrics? Or as...
  38. O

    MHB Calculating partial derivatives in different coordinate systems

    let f = x2 + 2y2 and x = rcos(\theta), y = rsin(\theta) . i have \frac{\partial f}{\partial y} (while holding x constant) = 4y . and \frac{\partial f}{\partial y} (while holding r constant) = 2y . i found these partial derivatives by expressing f in terms of only x and y, and then in...
  39. U

    Functions in coordinate systems

    Hi all. What does it mean that a function in polar coordinates may not be a function in Cartesian coordinates? For example, r(\theta) = 1 + \sin\theta is a function because each \theta corresponds to a single value of r. However, in Cartesian coordinates, the graph of this function most...
  40. W

    Coordinate Tetrads: Other than Cartesian?

    Dear Friends Is there any coordinate tetrad in spacetime except Cartesian basis ? since tetrad basis should be orthogonal (( In Lorentzian description ))and the only orthogonal basis is Cartesian ( the metric is (+1,-1,-1,-1 ) but in any other coordinate basis like Spherical metric is (...
  41. T

    Coordinate Geometry: PQRS Parallelogram

    I would like someone to give this a quick check, I am really not sure if I am over thinking this question. I got the right ans, just would like a quick check of my method; big thanks in advance. question: P(-1,5), Q(8,10), R(7,5) & S(x,y) are the veritices of the parallelogram PQRS. Calculate...
  42. D

    Cartesian to Cyclindrical Coordinate

    Problem Solution answer For this one, my upper bound of z in cylindrical's is sqrt(4-r^2) instead of (4-r^2). Which one is right, mine or the solution? Thanks for helping me out.
  43. Vorde

    Basis/Unit vectors in other coordinate systems

    We all know the ##\vec{i}##,##\vec{j}##,##\vec{k}## unit vectors for Cartesian space. But I've never been shown basis unit vectors in other coordinate systems. Do basis vectors exist in other coordinate systems? And if so what are they?
  44. H

    How to use Euler's angle theorem in rotation of a coordinate

    If i have a point at (0,0,5) in x,y,z system, then i make 2 rotation on the point with center at origin. i)the first rotation is on y-axis with angle P in clockwise direction. ii) the second rotation is on the point's new x-axis rotate in angle Q in clockwise direction. How can i find the...
  45. E

    Invariance of vectors due to changes in coordinate systems

    Homework Statement How do I know that vector is invariant to changes of coordinate systems if i only have the components of the vector and not the basis vectors? Homework Equations let the vector in reference frame 1 be ds and the same vector in the reference frame 2 be ds1 The...
  46. S

    How change from one to another coordinate system

    Hello! I have a problem. How can I convert a left part from picture which is in coordinate system (r, s) to coordinate system (x, y) and then to coordinate system (ζ, η) (right part). I need Jacobian matrix because of integration some function above this region. Any helpful links or...
  47. I

    Integral depending on coordinate differences

    Homework Statement Consider a function which depends only on a difference between two variables, and integrate it with respect to both: \int_a^b \int_a^b f(x-y)\, dxdy Is there any way to simplify this expression, like reducing it into a 1-D integral?
  48. A

    What does it mean that vector is independent of coordinate system

    Hi PF, I have always wondered what was meant when my teachers told me that a vector is the same no matter what coordinate system it is represented in. What is it exactly that is the same? I mean the components change. So the only thing that I can see remains the same is the length of the vector...
  49. W

    Flux in different coordinate systems

    I have an electromagnetic field with a Poynting vector that has the following form in spherical coordinates: $$\bar{P}(R,\phi,\theta)=\frac{f(\phi,\theta)}{R^2}\bar{e}_{r}$$ The exact nature of f(\phi,\theta) is not known. Suppose I measure the flux of this vector field by a flat area...
  50. L

    Differential operators in arbitrary coordinate systems?

    Hi, physics undergraduate here. I don't know much about differential geometry yet, but I'm curious about this idea: Say I encounter a boundary value problem, and I'm not sure what coordinate system would be 'easiest' to solve the problem in. Is there some way to put the differential...
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