Coordinate Definition and 868 Threads

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...

I am reading Differential Topology by Guillemin and Pollack. Definition: X in RN is a k-dimensional manifold if it is locally diffeomorphic to Rk. Suppose U is an open subset of Rk and V is a neighborhood of a point x in X. A diffeomorphism f:U->V is called a parametrization of the...

Homework Statement Locate the x coordinate such that E=0? Coulomb constant is 8.98755x10^9 N m^2/C^2. The 1.68x10^-6 charge is at the origin and a -8.54x10^-6 charge is 10 cm to the right, as shown in the figure. http://i325.photobucket.com/albums/k398/bdh1613/018.jpg Locate the x...

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...

Is the following correct, as far as it goes? Suppose I have a vector space V and I'm making a transformation from one coordinate system, "the old system", with coordinates xi, to another, "the new system", with coordinates yi. Where i is an index that runs from 1 to n. Let ei denote the...

Homework Statement An observer in an inertial reference frame S sees two cameras flash simultaneously. The cameras are 800 m apart. He measures that the first flash occurs at four coordinates given by X1=0, Y1=0, Z1=0 and T1=0, and that the second flash occurs at four coordinates given by...

Homework Statement Given Cartesian coordinates x, y, and polar coordinates r, phi, such that r=\sqrt{x^2+y^2}, \phi = atan(x/y) or x=r sin(\phi), y=r cos(\phi) (yes, phi is defined differently then you're used to) I need to find \frac{d\phi}{dr} in terms of \frac{dy}{dx} Homework...

Hi there. This isn't so much a math question as it is a conceptual question. I can't seem to wrap my head around the need for coordinate transformations. *Why* do they need to be done? I think I really need a picture for this, so this might not be the right place to ask, but if you can...

A friend asked me this question today. It kinda threw me for a loop. The cartesian coordinates system is a left handed coordinate system right, so therefroe they are defined by a left handed coordinate syste correct?

In defining a coordinate chart, \left ( U,\phi \right ), U \in M, \phi : U \to \mathbb{R}^{n}, on a manifold M, what exactly is \mathbb{R}^{n}: the set of all n-tuples, a topological space, a metric space, a vector space, Euclidean space conceived of as an inner product space, Euclidean...

Homework Statement Show that the electric field of a "pure" dipole can be written in the coordinate-free form E_{dip}(r)=\frac{1}{4\pi\epsilon_0}\frac{1}{r^3}[3(\vec p\cdot \hat r)\hat r-\vec p]. Homework Equations Starting from E_{dip}(r)=\frac{p}{4\pi\epsilon_0r^3}(2\cos \hat r+\sin\theta...

I have that P is the tangent plane to the surface xyz=a^{3} at the point (r,s,t). I need to show that the volume of the tetrahedron, T, formed by the coordinate planes and the tangent plane to P is indepedent of the point (r,s,t). I have found that P is; \frac{x}{r} + \frac{y}{s} +...

HELP! Setting up triple integral in spherical coordinate Homework Statement http://img517.imageshack.us/img517/9139/83291277.jpg Homework Equations I set up the bound for this problem as following: r=0..2/cos(phi), phi=pi/2..3pi/4, theta=0..2pi, but maple always return an error in...

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...

Homework Statement The actual question is to evaluate the integral. All I need help on is the setting up part. Instead of making a thread for each, I will post 3 integral question with my attempts. Just tell me if you see something wrong from rectangular to spherical conversion...

Homework Statement change from rectangle to spherical coordinate : z^2 = x^2 + y^2 I know that : z = pcos(phi) x = psin(phi)cos(theta) y = psin(phi)sin(theta) there fore z^2 = x^2 + y^2 in spherical coordinate is p^2cos(phi)^2 = (psin(phi)cos(theta))^2 +...

Homework Statement evaluate : \int\int\int_{E} e^z DV where E is enclosed by the paraboloid z = 1 + x^2 + y^2 , the cylinder x^2 + r^2 = 5 I just need help setting this up. I know that theta is between 0 and 2pi Now is z between 0 and 1 + r ? and r is between 0 and sqrt(5)...

Homework Statement can you explain this conversion, I am not sure. Rectangle coord : \int^{2}_{-2}\int^{sqrt(4-x^2)}_{-sqrt(4-x^2)}\int^{2}_{sqrt(x^2 + y^2 )} F(x) dzdydx = cylindrical coord : \int^{2\pi}_{0}\int^{2}_{0}\int^{2i}_{r} r*dzdrd\theta I see that x^2 + y^2...

Homework Statement In the xy-plane, sketch the coordinate system [ a; b] corresponding to the basis { (1, 1 ) , (1, -1) } by drawing the lines a = 0, \pm1 and b = 0, \pm1. What point in the xy-plan corresponds to a = 1, b = 2?Homework Equations Not sure of any in this caseThe Attempt at a...

In Misner, Thorne, Wheeler: "Gravitation" it is stated on that "no one has discovered a way to make an imaginary coordinate work in the general curved spacetime manifold" (p.51). Can anyone elaborate on this? Right now, I don't get why it wouldn't work and nothing more is said in the book.

Homework Statement A pendulum consists of a particle of the mass m and a thread of the length l (we don't consider the threads mass). The acceleration caused by gravity is g. Solve the particles displacement and the force caused by the tension in the thread T in a polar coordinate system. The...

Hey, I am having trouble understanding how you can transform one set of coordinates into another using partial derivatives i just don't get the whole thought process behind it. I came across this while reading about covariant and contrivariant vectors. If anyone can help clear up how this works...

"Simple" Coordinate Problem Homework Statement The following happens on a 2D X-Y Plane. A particle accelerates at {3t m/s2}i + 4t m/s2}j where t = seconds At t = 0, the position of the particle is {20.0 m}i + {40.0m}j At t = 0, the velocity of the particle is {5.00 m/s}i + {2.00 m/s}j At...

Homework Statement On a supermarket parking lot, a car is pulling out and bumping into an oncoming car. The car pulls out with 0.8 m/s, while the oncoming car has a speed of 1.2 m/s. The angle between the velocities is 24 degrees, as indicated in the figure. What is the collision speed...

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...

What is Galileian system of coordinate? I have read the chapter about it by einstein but still can't understand it. Can anyone kindly explain it to me? thanks

Homework Statement Two in-phase loudspeakers are located at (x, y) coordinates (-3.0, +2.0) and (-3.0, -2.0) . They emit identical sound waves with a 2.0 m wavelength and amplitude a. Determine the amplitude of the sound at the five positions on the y-axis (x=0): with y=0.0 with y=0.5 with...

If a system is rotated around Z axis then the new coordinates are X'= xcos() - Y sin(), Y'= Xsin() + Ycos() Z'= Z How is this obtained ?? () --->theta , angle of rotation around Z axis .

Homework Statement 2 coordinate systems are given: 1st: \vec{a}, \vec{b}, \vec{c} 2nd: \vec{m}, \vec{n}, \vec{p} in system \vec{a}, \vec{b}, \vec{c} basis vectors of 2nd system have values: \vec{m}=\{2/3, 1/3, 1/3\}, \vec{n}=\{-1/3, 1/3, 1/3\}, \vec{p}=\{-1/3, -2/3, 1/3\} also known that...

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...

I want to caculate length of curve in Polar coordinate system like this: if r=r(a) then length of the curve is [SIZE="4"]∫r(a)da Is this right? if not ,why ? What's the right one ? I konw the way in rectangular coordinate system,I just want to do it in Polar coordinate system .

Can anyone explain why it's important to be able to take vectors in an x,y,z coordinate system and be able to transform them into other coordinate systems. Could not all vector considerations be grappled with in the standard x,y,z coordinate systems? How important is this ability to physicists...

So here's how it goes. Find the coordinates of the centre and the radius of the circle x^2 + y^2 - 4x + 6y -12 =0 a)If the circle cuts the x-axis at the points A and B , find the length of line segment AB. My question is , I have actually found 2 points , they are (-2,0) and (6,0)...

Homework Statement Prove: Let A \in \mathrm{M}_{n \times n}(\mathbb{F}) and let \gamma be an ordered basis for \mathbb{F}^n . Then [\boldmath{L}_A]_{\gamma} = Q^{-1}AQ , where Q is the nxn matrix whose jth column is the jth vector of \gamma . Homework Equations \boldmath{L}_A...

Anyone have a good link to a site explaining the different coordinate systems and the jacobian determinant for each of them. Thanks EDIT: I actually just need a website wiht a list of the different transformations ie. polar: x = u*cos(v) y = u*sin(v) v \in [0,2\pi], u \in [0,radius] J = r

I do not understand Spherical coordinate system. I'm asked to compare the differences with Cartesian coordinate but I have no idea how to start. So I would like some help that will at least give me a understanding of the spherical coordinate system, thx

Could someone plase hep me with normal coordinate substitutions with periodic boundary conditions, I can't see where the 1/N cancels in the attached file Thanks Doug

I would attempt to solve these questions with "relevant equations", but my questions simply derive from an attempt of understanding class notes. If someone could attempt to help my understanding, that would be great. I've attached the PDF file that contains my corresponding questions...

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...

Does "coordinate system" = "gauge"? [SIZE="4"]Are "coordinate system" and "gauge" the same thing? What about "coordinate transformation" and "gauge transformation"?

http://img208.imageshack.us/img208/5153/12802868.png Why is the del operator for cylindrical coordinate the upper one and not the lower one? How does the 1/r term arises?

Hi all: I am wondering if there is any book or course note about the geometry in spherical coordinate. Not just the superficial definition and the convertion with Euclidean coordinate. But something like how a line is defined in spherical coordinate in 3D space, how a plane is defined, how to...

Help me Evaluate the iterated intergal by converting to polar coordinate: http://www.ziddu.com/gallery/4894419/Untitled.jpg.html

Hi Guys, I have been given the coordinates of a cylinder inside a sphere and want to convert to Cylindrical coordinates to compute the volume of the cylinder. Can you please check the limits and integral I have? The cylinder is x^2+y^2= 4 sphere = x^2+y^2+z^2= 9 As its a cylinder...

Any relationship between mass, length and time in general relativity can be considered using tensors of Einstein's Field Equations which are independent of the coordinate system used and of the origin of that coordinate system Is there a formal name for such coordinate independence and origin...

Homework Statement Find the area inside one leaf of the four-leaved rose r = cos2xHomework Equations A = 1/2 antiderivative abr2 dxThe Attempt at a Solution I just need help in finding the lower and upper limits of integration. But besides that, I know how to do the rest. If my integration is...

Hi all! I am studying the Galilean group of transformations and I'm not sure how to transform the Nabla operator. Consider the 2 transformations: (x,t)->(x+s,t) (x,t)->(Dx,t) and the expression "nabla (x)" where D is a matrix and x, s are vectors I am pretty sure that I have...

I'm looking, as an observer, at imaging accretion discs and tori around Kerr black holes. The image of the disc/torus is projected onto a 2D grid (a CCD if you like) so all lensing effects etc. are implicit. Basically, I can plot the image after determining the (x,y) coordinates in the 2D grid...

Note: The derivatives are partial. I've seen the coordinate transformation equation for contravariant vectors given as follows, V'a=(dX'a/dXb)Vb What I don't get is the need for two indices a and b. Wouldn't it be adequate to just write the equation as follows? V'a=(dX'a/dXa)Va...

In geometry the change of variable, x = (2 / sqrt(5))x' - (1 / sqrt(5))y' (#1) y = (1 / sqrt(5))x' + (2 / sqrt(5))y' (#2) can be used to transform the equation 2x^2 - 4xy + 5y^2 = 1 into the simpler equation (x')^2 + 6(y')^2 = 1, in which form it is easily seen to be the...