Coordinate systems Definition and 120 Threads

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. F

    Choice of Origin of Coordinate Systems

    I am having a personal discussion with somebody elsewhere (not on Physics Forums) and we are stuck at the moment because of a disagreement that I narrowed down to the question whether, in the context of SR, two observers in different reference frames can choose the origin of their coordinate...
  2. Z

    Why Does General Relativity Use Coordinate Systems?

    If you look at Newtonian gravity, there is no major deal with coordinate systems. I am guessing we use coordinate systems because in general relativity we think of coordinate systems as different frames of references and that all frame of references must have the same laws of physics. Is that why?
  3. Ahmad Kishki

    Vectors in different coordinate systems

    how do i write vectors in polar coordinate? And what will the azimuth coordinate represent? I was trying to figure out the vector connecting a ring to its center using polar coordinates, so that i would perform an integration over d(phi) (finding the electric field due to a semicircle at the...
  4. U

    Can I use 2 different coordinate systems for one system?

    Homework Statement As shown in the image below, can I use 2 different co-ordinate systems when drawing the free body diagram for each object? Homework Equations The Attempt at a Solution
  5. C

    Mapping Coordinate Systems Using Quaternions

    During the course of working with inertial measurement units (IMU) I have run into a problem. The issue is that an IMU reports accelerations relative to the IMU's orientation rather than it's initial orientation. The IMU's initial orientation is the identity quaternion (1,0,0,0). All changes...
  6. F

    Angle between two orthogonal coordinate systems

    If two orthogonal coordinate systems (xyz and x'y'z') share a common origin, and the angles between x and x', y and y', and z and z' are known. What is angle between the projection of z' on the xy plane and the x axis? Thank you for your help!
  7. zdcyclops

    Emergent coordinate systems in quantum physics

    Do unobserved particles exchange information with other particles? If not then they are not only unobserved but also un-observing, which would seem to mean that they not only do not have a well defined position but that the very concept of position does not exist for them, nor does distance or...
  8. A

    Cross products for unit vectors in other coordinate systems

    I am a bit confused often when I have to compute cross products in other coordinate systems (non-Cartesian), I can't seem to find any tables for cross products such as "phi X rho." in spherical I think that these unit vectors are considered to be "perpendicular," so would phi X rho just be "+/-...
  9. M

    A mechanics problem with moving and fixed coordinate systems

    [b]1. A point P is described in terms of a fixed coordinate system XYZ with unit vectors I,J,K and a moving coordinate system xyx with unit vectors i,j,k.at a given instant the location of the origin of the moving system is 80I-90J.the velocity of P relative to moving system is 50i+45j;the...
  10. ShayanJ

    How Do Different Coordinate Systems Affect Vector Operations?

    Recently I've been studying about orthogonal coordinate systems and vector operations in different coordinate systems.In my studies,I realized there are some inconsistencies between different sources which I can't resolve. For example in Arfken,it is said that the determinant definition of the...
  11. R

    Are Oblique Coordinate Systems More Useful Than Orthogonal Systems in 2-D Space?

    In a coordinate system two axes are inclined at an acute angle θ. Is this coordinate system different from a coordinate system in which the axes are inclined at an angle (180 - θ)? if we look at the four quardents in either of the above set of axes, both are included giving the impression that...
  12. L

    Is the given unit vector derivation valid for any coordinate system?

    ## \vec{r}=\rho \cos \varphi \vec{i}+\rho \sin \varphi \vec{j}+z\vec{k} ## we get \vec{e}_{\rho}=\frac{\frac{\partial \vec{r}}{\partial \rho}}{|\frac{\partial \vec{r}}{\partial \rho}|} \vec{e}_{\varphi}=\frac{\frac{\partial \vec{r}}{\partial \varphi}}{|\frac{\partial \vec{r}}{\partial...
  13. M

    2 Rotations on different coordinate systems

    I have a question that i been trying to solve which seam simple but been having trouble. Today I thought about rotation matrix and how the following problem would be solved. Initial Coordinate system (x,y,z) a rotation is desired about x let's say α=30 degrees so that a new coordinate...
  14. B

    How Can You Derive x, y, & z Coordinates in Various Orthogonal 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...
  15. 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...
  16. 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}...
  17. 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...
  18. 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...
  19. U

    Can a Function in Polar Coordinates Fail in Cartesian Coordinates?

    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...
  20. 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?
  21. 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...
  22. 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...
  23. 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...
  24. U

    Integration in two different coordinate systems

    Hi all. I am very puzzled by the following. Let x_1 and x_2 be two coordinate systems related by x_1=1-x_2. Now if y(x_1) = x_1 and z(x_2) = 1-x_2, then clearly y(x_1)=z(x_2). Now integrating the function in each coordinate system gives Y(x_1) = \int y(x_1) dx_1 = \int x_1 dx_1 =...
  25. T

    Relationship between two coordinate systems.

    Homework Statement http://img15.imageshack.us/img15/1671/capturetwy.png The Attempt at a Solution Could someone please explain what is meant by "if v is constrained to 0"? Also how do you find a relationship between two axis of different coordinate systems? I really have no clue where...
  26. O

    Coordinate Systems: When to Make the Switch?

    We may solve a function or check a theorem but sometimes the mathematics is easier when we switch from different coordinate systems. What can we look for that tells us changing is a good idea?
  27. S

    Right-handed, left-handed systems for different coordinate systems, et al

    I know the orientations of the x-, y- and z- axes for a right-handed and a left-handed system. But that's for the cartesian coordinate system. How are the orientations of the coordinate axes for other coordinate systems defined? Also, i X j = k, j X k = i and k X i = j. How does this apply...
  28. P

    The relationship between coordinate systems and reference frame

    Hi there, I am confused about the relationship between coordinate systems and reference frame in GR. I understand the coordinate systems can be used to describe reference frames, for example, Local inertial frames in GR can be defined by Riemann Normal Coordinates. However, take the...
  29. 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...
  30. 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...
  31. 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.
  32. 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...
  33. 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"...
  34. L

    Can You Combine Basis Vectors from Different 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.
  35. S

    Coordinate Systems Homework: Prove \nabla.\vec{r}=3

    Homework Statement For the cartesian, cylindrical, spherical coordinate system, prove that \nabla.\vec{r} = 3 and \nablax\vec{r}=0 Homework Equations For cylindrical coord system, \vec{r} = s\vec{s} + z\vec{z} \nabla = \vec{s} \delta/\deltas +...
  36. U

    Mechanics: Coordinate systems and vector's

    Homework Statement An ant walks from the inside to the outside of a rotating turntable. Write down it's velocity vector. Use polar the cartesian coordinates. Homework Equations I have already derived the velocity vector in polar coordinates which is: \hat{v} = \dot{r}\hat{r} +...
  37. B

    Partially rotated coordinate systems

    Hello, I am trying to understand this partially rotated coordinate systems. I do not understand how does x'=xcos(theta)+ysin(theta) and y'=ycos(theta)-xsin(theta) I am probably stuck at silly answer but i need this to understand deriving of formulas for special relativity. Thanks
  38. H

    Vectors with different coordinate systems

    Hi, I am trying to simulate a freely jointed chain polymer to do that I want to put several rods (length a) on top of each other but with different angles. My problem is like this I have a vector(1) and at the end of this vector(1) I put another vector(2), the z-axis of this vector(2)'s...
  39. M

    Simultaneity in General Relativity and Problem with coordinate systems concepts.

    Hi there, Physics lovers. I'm studying "The Classical Theory of Fields" from the "Course of Theoretical Physics" book series by Lev D. Landau, and I'm stuck with simultaneity in General Relativity. In page 251 of the Fourth "revised" english edition, by Butterworth Heinemann, There begins the...
  40. T

    Can a Matrix A Equalize Vectors u and v in Different Reference Frames?

    Hi everyone, Given two different reference frames in a vector space; say left and right. v is a vector defined in the left frame and u is a vector defined in the right frame. What is the nature of a matrix A that can satisfy the equality u= A.v? Thank you
  41. Jonnyb42

    Coordinate Systems: GR vs Newtonian

    I just want to ask a simple question: Is it true that Newtonian/Classical Mechanics does not hold true for all coordinate systems, while General Relativity does?
  42. K

    Working with different coordinate systems

    Does anyone know of a good book for relearning and working with different cooridinate systems like polar cylindricaly spherical the typicall engineering stuff...
  43. M

    What are the general requirements for defining a coordinate system in R^3?

    Say we have a vector field defined in R^3. That is, at every point p in R^3, we have the corresponding set (p, v(p)). In representing this field, as far as I can tell, we have a certain list of very general requirements. That seems to be a.) an origin, b.) three everywhere non-coplanar curves...
  44. S

    Playing with Coordinate Systems (Spherical Geometry)

    I'm working on a problem that involves two Earth stations that scan the skies. I'm writing a simulation program (no physics involved) that simply finds the az/alt of an event observed simultaneously by each station. At this point, I'm warming up to the mathematics, spherical geo, etc. to pull...
  45. D

    Coordinate systems in the solar system?

    I have read the wikipedia page regarding Celestial coordinate systems and searched on google, but I cannot find any coordinate systems which describe a planet's position in it's orbit. Does there exist such a system? An example use of this system would be in locating the planets in the sky. I...
  46. J

    Understanding the 3 coordinate systems for a Schwarzschild geometry

    Hello, There are 3 main coordinate systems for a Schwarzschild geometry : Lemaitre-Rylov (LR), Eddington-Finkelstein (EF), Kruskal-Szekeres (KS). Thanks to my readings, I know thaht KS coordinates are better than EF coordinates and that EF coordinates are better than LR coordinates. But, I...
  47. S

    Coordinate systems for electric fields.

    Im curious about an electric field (somewhere of radius s) inside a solid sphere (radius a) such that: \int E.da=E4\pi s^{2} and Q = \frac{\rho 4\pi s^{3}}{\epsilon_{o}3} What is the difference between using each coordinate system to solve for E? It's just that I've really had to teach...
  48. 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...
  49. 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...
  50. 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...
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