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. jisbon

    Calculating coordinates of intercepts from field of view to target

    Say we are working in a 2D plane, with a camera and a ball flying past as shown. Camera at bottom, ball flying from left to right Given that I have the X/Y coordinates of the camera, as well as the coordinates of the ball at any given time during the 'flight', how am I supposed to calculate the...
  2. D

    I Exploring the Flexibility of Coordinates in Euler-Lagrange Equations

    Hello all, so I’ve been reading Jennifer Coopersmith’s The Lazy Universe: An Introduction to the Principle of Least Action, and on page 72 it says: If I understand it right, she’s saying that in our Euler-Lagrange equation ## \frac {\partial L} {\partial q} - \frac {d} {dt} \frac {\partial L}...
  3. e2m2a

    I Analyzing Dynamics in Constant Acceleration w/Rindler & Equivalence

    Not sure when to use Rindler coordinates to analyze dynamics in a constant accelerating reference system. Rindler coordinates seem messy because they are always changing. Wouldn't it be easier to invoke the principle of equivalence and treat the environment of an accelerating system as a...
  4. Stefan H

    A Solving Laplace's equation in polar coordinates for specific boundary conditions

    Hello everybody, Currently I am doing my master's thesis and I've encountered a physics problem which is very difficult for me to solve. The problem I have is finding equations for the magnetic scalar potential inside and outside a ferromagnetic wire for specific boundary conditions...
  5. A

    When to use the Jacobian in spherical coordinates?

    Greetings! here is the solution which I undertand very well: my question is: if we go the spherical coordinates shouldn't we use the jacobian r^2*sinv? thank you!
  6. curiousPep

    I Lagrangian mechanics - generalised coordinates question

    I think I undeerstand Lagrangian mechanics but I have a question that will help to clarify some concepts. Imagine I throw a pencil. For that I have 5 generalised coordinates (x,y,z and 2 rotational). When I express Kinetic Energy (T) as: $$T = 1/2m\dot{x^{2}}+1/2m\dot{y^{2}}+1/2m\dot{z^{2}} +...
  7. uzi kiko

    Python Numerical integration over a disk with polar coordinates

    In my job, I was given the task of calculating a force that operates an ultrasound transmitter on a receiver. The calculation is made by assuming that each point on the transmitter is a small transmitter and integration should be made on the surface of the transmitter. Since the transmitter is...
  8. L

    I Understanding Special Relativity and Coordinates

    I'd like to get some help on checking my understanding of special relativity, specifically I'm trying to clarify the idea of coordinates. Any comment is really appreciated! The spacetime is an affine space ##M^4##, which is associated with a 4 dimensional real vector space ##\mathbb{R}^4##...
  9. ektov_konstantin

    I Moving center of coordinates in the polar graph

    I have a function in polar coordinates: t (rho, phi) = H^2 / (H^2 + rho^2) (1) I have moved the center to the right and want to get the new formulae. I use cartesian coordinates to simplify the transformation (L =...
  10. L

    I Benefits of Lagrangian mechanics with generalised coordinates

    I have sometimes seen the claim that one advantage of Lagrangian mechanics is that it works in any frame of reference, instead of like Newtonian mechanics which will hold only in the inertial frame of reference. However isn't this gain only at the sacrifice that the Lagrangian will need to take...
  11. Mayhem

    Deriving the Laplacian in spherical coordinates

    As a part of my self study, I am trying to derive the Laplacian in spherical coordinates to gain a deeper understanding of the mathematics of quantum mechanics. For reference, this the sphere I am using, where ##r## is constant and ##\theta = \theta (x,y, z), \phi = \phi(x,y)##. Given the...
  12. P

    A Comparing Gullstrand-Painleve & Lemaitre Coordinates

    For reference, the wikipedia entries are adequate for this discussion: https://en.wikipedia.org/wiki/Gullstrand–Painlevé_coordinates (henceforth, GP coordinates) https://en.wikipedia.org/wiki/Lemaître_coordinates (henceforth, LM coordinates) Both of these coordinates are based on a foliation...
  13. Danielle46

    I have to prove that vectors in spherical coordinates are clockwise

    I should use the cross product but I don´t know how. I tried to calculate it but it didn´t work out as expected. Please can you give me one example how to do it ?
  14. Tapias5000

    How can I locate the coordinates of the centroid of a cone in Z?

    This is the picture of the problem. My solution is: I'm not sure if the limit is 0 to 2 or 0 to 4...
  15. cianfa72

    I Clarification on Rindler coordinates definition

    Hi, starting from this post Basic introduction to gravitation as curved spacetime I would ask for a clarification about Rindler coordinates. From this wiki entry Rindler coordinates I understand that the following transformation (to take it simple drop ##y,z##) $$T = x\sinh{(\alpha t)} ...
  16. j19063dc

    Finding the resultant force, moment, and x-y coordinates

  17. K

    A Cyclic coordinates in a two body central force problem

    (Goldstein 3rd edition pg 72) After reducing two body problem to one body problem >We now restrict ourselves to conservative central forces, where the potential is ##V(r)## function of ##r## only, so that the force is always along ##\mathbf{r}##. By the results of the preceding section, I've...
  18. derya

    A Analytical solution for an integral in polar coordinates?

    Hi, I am trying to find open-form solutions to the integrals attached below. Lambda and Eta are positive, known constants, smaller than 10 (if it helps). I would appreciate any help! Thank you!
  19. Mathman2013

    Find the coordinates of a point C from the given line, point and circle

    Let the point P(2,8) be a point in xy-plane and line m: y = -0.75*x+3.25 be a line in the xy-plan. The distance from a point P to a point B is 7 unites. Where the x coordinate of B is negative. Find the acute angle between PB and m. To find B I then construct a circle of radius 7 with center...
  20. D

    I Scalar product and generalised coordinates

    Hi If i have 2 general vectors written in Cartesian coordinates then the scalar product a.b can be written as aibi because the basis vectors are an orthonormal basis. In Hamiltonian mechanics i have seen the Hamiltonian written as H = pivi - L where L is the lagrangian and v is the time...
  21. K

    I Independent coordinates are dependent

    (This is not about independence of ##q##, ##\dot q##) A system has some holonomic constraints. Using them we can have a set of coordinates ##{q_i}##. Since any values for these coordinates is possible we say that these are independent coordinates. However the system will trace a path in the...
  22. J

    3D Laplace solution in Cylindrical Coordinates For a Hollow Cylindrical Tube

    Here is the initial problem and my attempt at getting Laplace solution. I get lost near the end and after some research, ended up with the Bessel equation and function. I don't completely understand what this is or even if this i the direction I go in. This is a supplemental thing that I want to...
  23. Haorong Wu

    I Understanding Frequency in Rindler Coordinates for a Scalar Massless Field

    I consider a scalar massless field obeying the Klein-Gordon equation ##\Box \psi=0 ##. First, in Minkowski spacetime, a solution of the equation is $$ u_{\mathbf k}(x^\mu)=((2\pi)^3 2 \omega)^{-1/2} e^{ik_\mu x^\mu}$$ where ##\mathbf k=(\omega, \vec k)##. So this mode has a frequency of...
  24. p1ndol

    I Trouble understanding coordinates for the Lagrangian

    Hello, I'm having some trouble understanding this solution provided in Landau's book on mechanics. I'd like to understand how they arrived at the infinitesimal displacement for the particles m1. I appreciate any kind of help regarding this problem, thank you!
  25. A

    Double integral with polar coordinates

    Greetings! I have the following integral and here is the solution of the book (which I understand perfectly) I have an altenative method I want to apply that does not seems to gives me the final resultMy method which doesn't give me the final results! where is my mistake? thank you!
  26. Istiak

    How to find coordinates of a system (I am taking cylinder now)?

    A person wrote that ##L=\frac{1}{2} m (\dot{r}^2+r^2 \dot{\phi}^2 +\dot{z}^2)## But, how to find equation of that coordinate system?
  27. redtree

    I Fourier transform of a function in spherical coordinates

    I am trying to understand the relationship between Fourier conjugates in the spherical basis. Thus for two functions ##f(\vec{x}_3)## and ##\hat{f}(\vec{k}_3)##, where \begin{equation} \begin{split} \hat{f}(\vec{k}_3) &= \int_{\mathbb{R}^3} e^{-2 \pi i \vec{k}_3 \cdot \vec{x}_3} f(\vec{x}_3...
  28. M

    B Exploring Holonomic Basis in Cartesian Coordinates

    Are cartesian coordinates the only coordinates with a holonomic basis that's orthonormal everywhere?
  29. K

    Kepler problem in parabolic coordinates

    I solve (1). But to solve (2), What should be the suitable separation constants? I am so confused... E=2/(m*(a+b)) * (a*(dWa/da)^2+b*(dWb/db)^2-k)+l^2/(2mab) where l(constant) is pc since c is cyclic. What should I do to solve the problem?
  30. D

    I Question about the vector cross product in spherical or cylindrical coordinates

    Hi If i calculate the vector product of a and b in cartesian coordinates i write it as a determinant with i , j , k in the top row. The 2nd row is the 3 components of a and the 3rd row is the components of b. Does this work for sphericals or cylindricals eg . can i put er , eθ , eφ in the top...
  31. L

    A Tensor product in Cartesian coordinates

    I am confused. Why sometimes perturbation ##V'=\alpha xy## we can write as ##V'=\alpha x \otimes y##. I am confused because ##\otimes## is a tensor product and ##x## and ##y## are not matrices in coordinate representation. Can someone explain this?
  32. E

    Scale factors in spherical coordinates

    how they got that value for the scale factors h?
  33. I

    Vectors - finding coordinates of collision point

    For car 1, the parametric equations are x = 1 + 0.8t and y=t. For car 2, the parametric equations are x=0.6s and y=2+s. (Let t and s represent time). Solving the system of equations, when the x values are equated are the y values are equated, I get s = -13 and t = -11. I assume that the 2 cars...
  34. D

    I Vector squared in polar coordinates

    Hi I was always under the impression that i could write a2 = a.a = a2 Equation 1 where a⋅ is a vector and a is its modulus but when it comes to the kinetic energy term for a particle in plane polar coordinates I'm confused ( i apologise here as i don't know how to write time derivative with...
  35. Pipsqueakalchemist

    Engineering Using Cartesian vs. Normal/Tangential Coordinates for Centripetal Motion

    So for this problem the solution used Cartesian coordinates but I was wondering wouldn’t it be easier to use Normal and tangential coordinate because the bar is undergoing centripetal motion? Also on the right diagram shouldn’t the acceleration be down and not up. The reason I think that is...
  36. warhammer

    Basic question pertaining to Polar Coordinates & how to employ them

    I have a question that might be considered vague or even downright idiotic but just wanted to know that once we find out the velocity & acceleration of a body in angular motion in plane polar coordinates, and are asked to integrate the expressions in order to find position at some specified time...
  37. A

    Problem with a triple integral in cylindrical coordinates

    Good day here is the solution J just don't understand why the solution r=√2 has been omitted?? many thanks in advance best regards!
  38. yucheng

    Incorrect derivation of tangential acceleration in polar coordinates

    I am trying to derive the tangential acceleration of a particle. We have tangential velocity, radius and angular velocity. $$v_{tangential}= \omega r$$ then by multiplication rule, $$\dot v_{tangential} = a_{tangential} = \dot \omega r + \omega \dot r$$ and $$a_{tangential} = \ddot \theta r +...
  39. G

    A Laplace eq. in cylindrical coordinates and boundary conditions

  40. SebastianRM

    I How to obtain the determinant of the Curl in cylindrical coordinates?

    I have a vector in cylindrical Coordinates: $$\vec{V} = \left < 0 ,V_{\theta},0 \right> $$ where ##V_\theta = V(r,t)##. The Del operator in ##\{r,\theta,z\}$ is: $\vec{\nabla} = \left< \frac{\partial}{\partial r}, \frac{1}{r}\frac{\partial}{\partial \theta}, \frac{\partial}{\partial z}...
  41. R

    MHB Motion in polar coordinates

    I need a little help with this problem please
  42. E

    B Transform to accelerating coordinates

    It's a silly example, but hopefully it will help me to understand the maths. Two guys ##A## and ##B## are initially at the same spacetime event ##O##, and then ##B## receives an impulse along the ##x##-direction giving him an initial coordinate velocity ##\dot{x}_B = v_0## as measured by ##A##...
  43. J

    Linear chain of oscillators and normal coordinates

    Hello, I hope the equation formatting comes out right but I'll correct it if not. So far, I have attempted to write ##\ddot{a}_k(t) = \sum_{n}(u^{k}_n)^*\ddot{q}_n(t) ##. Then I expand the right hand side with the original equation of motion, and I rewrite each coordinate according to its own...
  44. L

    I Determine the Transformation from Cylindrical to Rectangular coordinates

    In physics is usually defined that in cylindrical coordinates ##\varphi \in [0,2 \pi)##. In relation with Deckart coordinates it is usually written that \varphi=\text{arctg}(\frac{y}{x}). Problem is of course because arctg takes values from ##-\frac{\pi}{2}## to ##\frac{\pi}{2}##. What is the...
  45. cwill53

    How to set bounds in cylindrical coordinates analytically?

    I'm trying to evaluate the following integral in cylindrical coordinates. $$\int_0^6 \int_0^{\frac{\sqrt{2}}{2}}\int_x^{\sqrt{1-x^2}}e^{-x^2-y^2} \, dy \, dx \, dz$$ After attempting to set the bounds in cylindrical coordinates, I got $$\int_0^6 \int_0^{\frac{\sqrt{2}}{2}}\int_{\rho \cos\varphi...
  46. AHSAN MUJTABA

    I Cosmology Comoving coordinates and observers

    I just want to visualize the math, any help would be appreciated. TIY
  47. LCSphysicist

    Linear algebra invertible transformation of coordinates

    ##A^{x'} = T(A^{x})##, where T is a linear transformation, in such way maybe i could express the transformation as a changing of basis from x to x' matrix: ##A^{x} = T_{mn}(A^{x'})##, in such conditions, i could say det ##T_{mn} \neq 0##. But how to deal with, for example, ##(x,y) -> (e^x,e^y)## ?
  48. randomphysicsguy123

    Vector Problem -- Addition of two vectors given in polar coordinates

    Doing a review for my SAT Physics test and I'm practicing vectors. However, I am lost on this problem I know I need to use trigonometry to get the lengths then use c^2=a^2+b^2. But I need help going about this.
  49. T

    B Can coordinates be functions in geometry?

    Hello there.Could coordinates be functions?For example in a n-manifold with (x1,...xn) let be the coordinates could they be functions of a coordinate system not belonging to the n-manifold?Or we could first use a coordinate system then have our results, and then have a second coordinate system...
  50. F

    I Dot product in spherical coordinates

    I'm learing about antennas in a course, and we are using Jin's Electromagnetic text. This isn't a homework problem, I'm just trying to understand what I'm supposed to do in this situation. This part of the text discusses how to evaluate a radiation pattern. One of the steps to evaluate the...
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