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. J

    Vector calc question - coordinate systems

    Homework Statement How do you derive the divergence in cylindrical coordinates by transforming the expression for divergence in cartestian coordinates? Homework Equations F = F_x i + F_y j + F_z k div F = ∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z (divergence in Cartesian coordinates) I need to transform...
  2. J

    Coordinate systems for divergence

    Homework Statement Compute the divergence in cylindrical coordinates by transforming the expression for divergence in cartestian coordinates. Homework Equations F = F_x i + F_y j + F_z k div F = ∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z ... (divergence in cartesian coordinates) I need to...
  3. S

    Coordinate Systems in Modern Interpretation of Relativity

    Hello, I've really been enjoying reading these forums the last couple of weeks, and finally decided to register to ask a question. This is an earnest question about what the modern interpretation is, and how I and another student of relativity can learn more about the modern understanding...
  4. S

    Graphing Coordinate Systems in R3: Spherical Equations and Inequalities

    Homework Statement Graph the surface in R3 Homework Equations Spherical equation \rho = 2asin(\varphi) The Attempt at a Solution I think its just a sphere with a radius of 2 _______________________________________________ Homework Statement Graph the solid whose given coordinates...
  5. H

    Conversion Between Coordinate Systems

    Hello, I've been stuck on this problem for awhile and I've tried googling up some solutions but I still cannot find an answer to this question. Homework Statement An x-y coordinate system is shown below. A second system, u-v, is also shown. What is the relationship between the u-coordinate...
  6. DrGreg

    Accelerated coordinate systems

    This is in response to the following in another thread: I answer it here to avoid diverting that other thread's course. I'm assuming that Fredrik refers to using the plane of simultaneity of the co-moving inertial observer as a means of assigning coordinates to events in an accelerating...
  7. P

    Converting between coordinate systems?

    Homework Statement I have a bit of a general question, and I don't know whether or not the problem has a solution, but here's the idea behind it. I have two coordinate systems, let's call them CS A, and CS B. I have an infinite set of corresponding points for each system (both are 3D, so I...
  8. E

    Right-handed coordinate systems

    Homework Statement Everyone tells me that I should use right-handed coordinate systems. But no one tells me what happens if I don't. What is the danger of not using right-handed coordinate systems?Homework Equations The Attempt at a Solution
  9. M

    Rolling Cone - (Rotating Coordinate systems)

    Homework Statement A cone rolls on a flat surface. The instantaneous axis of rotation lies parallel to the point where the cone touches the surface and the angular velocity OMEGA. The motion of the center of mass (Vcm) plus a rotation OMEGAcm about the center if mass. Describe this motion by...
  10. G

    Relativity: Inertial vs. Coordinate Systems Explained

    Can anyone explain me what is the difference between inertial system and coordinate system in relativity? Please make me understand.
  11. R

    3 dimension coordinate systems

    Homework Statement Describe in words the region of R3 (3 dimension) represented by the following inequality. 1)xyz=0 Homework Equations none i know of The Attempt at a Solution no idea where to start. I know that this means one variable must be equal to 0, but i don't...
  12. D

    Any Standard Notation for Multiple Coordinate Systems?

    Homework Statement Given variables in one coordinate system, give the notation used to refer to the variables in another system. The known variable is x Homework Equations The transformation is an arbitrary one. My question has to do with notation and not mathematical procedures...
  13. Q

    Converting from 2D coordinate Systems

    I am trying to get from one 2D coordinate system to another 2D coordinate system. I found 2 corresponding points and each system. I did the following: [a1 a2 ] * [ x1,y1 ] = [u1,v1] [a3 a4] [ x2,y2] [u2,v2] or A*x = u if I use MATLAB to...
  14. B

    Coriolis forces, rotating coordinate systems

    I know that some people worship Symon's Mechanics 3rd Ed., but I find this book incredibly confusing...especially chapter 7, dealing with rotating coordinate systems. I follow the math, and perhaps the logic, but I can't even find a way to start the homework problems. The guy doesn't give any...
  15. F

    Dot product of basis vectors in orthogonal coordinate systems

    I'm doing a series of questions right now that is basically dealing with the dot and cross products of the basis vectors for cartesian, cylindrical, and spherical coordinate systems. I am stuck on \hat R \cdot \hat r right now. I'll try to explain my work, and the problem I am running into...
  16. B

    3-D coordinate systems problem

    Pleas help me with this exercises(this is not a homework): Determine whether the points lie on a straight line. a) A(5,1,3), B(7,9,-1), C(1,-15,11) b) K(0,3,-4) L(1,2,-2), M(3,0,1) Should I draw the graph, then find the slopes? Or is there any other way to approach? Pleas help...
  17. M

    Vectors and Coordinate Systems

    Hi, I'm a first year university student and I don't understand vectors and the coordinate system. I tried reading the book, but it doesn't make sense to me like the magnitude of theta and sigma or the oval with the vertical line through it. If someone could help me with the concept of it and...
  18. W

    Cylindrical and Spherical Coordinate systems

    I have a question about the equation mechanics of cylindrical and spherical coordinate systems This is basically about the velocity and acceleration equations of both Let me just give an example from cylindrical \vec v = \dot r\hat e_r + r\dot\theta\hat e_\theta + \dot z\hat k and...
  19. S

    Div an curl in different coordinate systems

    To calculate the divergence of a vectorfield in cartesian coordinates, you can think of it as a dot product, and to calculate the curl, you can think of it as a cross product. But how can you calculate the div and curl when you have spherical or cylindrical coordinates, without explicitely...
  20. M

    World-sheets, manifolds, and coordinate systems

    I'm trying to understand the manifold properties of world-sheets in string theory. I'm told that world sheets are manifolds and that manifolds are locally Euclidean. So I would like to know the characteristics between the space-time coordinates of the world-sheet given as xμ verses the 2D...
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