Coordinates Definition and 1000 Threads

Hi, I'm trying to find the area of a segment of a circle that is not at the origin. It will look similar to this picture below but I need to find the area enclosed by a circle. Using the polar equation of a circle provided by wikipedia: and integrating to find the area of a...

Hello all. I am trying to change: E = (1/r) ar To rectangular coordinate system. Where ar is a unit vector. So I know r = √(x^2 + y^2) i also think ar = ax+ay, where ax and ay are unit vectors along the x-axis and y-axis respectively. So that would give me: E = (1/√(x^2 + y^2)) (ax...

Homework Statement from the cartesian definition of angular momentum, derive the operator for the z component in polar coordinates L_z = -ih[x(d/dy) - y(d/dx)] to L_z = -ih(d/dθ) Homework Equations x = rcosθ y = rsinθ r^2 = x^2 + y^2 r = (x^2 + y^2)^1/2 The Attempt at...

Homework Statement On a treasure map, A = -5 (km)x + 2 (km)y, B = 4 km, and theta = 328 deg. The treasure is located at C = 4A - 3B. What is the x-coordinate of the treasure? What is the y-coordinate of the treasure? Homework Equations a^2 + b^2 = c^2 Vector addition The...

Homework Statement The total energy may be given by the hamiltonian in terms of the coordinates and linear momenta in Cartesian coordinates (that is, the kinetic energy term is split into the familiar pi2/2m. When transformed to spherical coordinates, however, two terms are angular momentum...

From this equation x2 + y2 = 2y I was wondering how in the solutions manual it was decided that 0≤z≤1 ? Edit: Don't read... I was looking at a solution to a different problem

A text I am reading displays the attached image. Can someone explain the general method for obtaining the velocity analogues of those terms (in parentheses) in 1.5? I know the second and third terms in parentheses in 1.6 and 1.7 are the squares of angular velocities, but can a general procedure...

Homework Statement The surface is x^2/y*z=10. Put this into cylidrical coordinates. in the form r=f(theta,z) Homework Equations No clue The Attempt at a Solution No clue

Homework Statement At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of i = (3.00 i - 2.00 j) m/s and is at the origin. At t = 2.70 s, the particle's velocity is = (9.30 i + 6.90 j) m/s. (a) Find the acceleration of the particle at any time t. =...

Homework Statement As a part of bigger HW problem, I need to calculate the integral: \oint[\hat{r}+\hat{z}]d\phi Homework Equations The Attempt at a Solution In cylindrical coordinates: =[\hat{r}+\hat{z}] \ointd\phi =2∏[\hat{r}+\hat{z}] On the other hand if I convert it to...

No idea how to do this. An object moving with uniform acceleration has a velocity of 11.0 cm/s in the positive x-direction when its x-coordinate is 2.91 cm. If its x-coordinate 2.75 s later is −5.00 cm, what is its acceleration? The answer is -10.1 cm/s squared but I don't know how to get...

Hey Guys, Does anyone know where I can find a derivation of the laplace operator in spherical and cylidrical coordinates?

Homework Statement We are given a function defined by x = uv, y = 1/2 (u^2-v^2)Homework Equations I derived the line element ds^2 = (u^2+v^2) dv^2 + (u^2+v^2) du^2 However I decided this was to unwieldy to derive our circumference where C = 2*{R}\oint_{-R}^{R} ds So I decided to try to...

Homework Statement Convert the following as indicated: 1. r = 3, θ = -π/6, φ = -1 to cylindrical 2. r = 3, θ = -π/6, φ = -1 to cartesian The Attempt at a Solution I just want to check if my answers are correct. 1. (2.52, -π/6, 1.62) 2. (-2.18, -1.26, 1.62)

we have a well known and simple equation for curl in cartesian coo. now we want it in let's say cylindrical coordinates. question is...can we transform every thing to cylinderical and then use the formula for cartesian?I mean writing basis vectors of cartesian in terms of r and theta and z and...

Hello, the definition of diffeomorphism is: a bijection f:M\rightarrow N between two manifolds, such that both f and f-1 are smooth. Is it thus correct to say that a (admissible) change of coordinates is a diffeomorphism between two manifolds?

I was given the problem r=2sin(2(θ)). I'm supposed to write the equation in the Cartesian Coordinates. I understand the basics to this but I'm not really sure how I'm supposed to write the equation when I have x=2sin(2(θ))cos(θ) and y=2sin(2θ)sin(θ).

Homework Statement Show that the vector fields A = ar(sin2θ)/r2+2aθ(sinθ)/r2 and B = rcosθar+raθ are everywhere parallel to each other. Homework Equations \mathbf{A} \cdot \mathbf{B} = |\mathbf{A}||\mathbf{B}|\cos(0) The Attempt at a Solution So, if the dot product equals 1. They should be...

Homework Statement The transformation from cartesian coordinates to cylindrical coordinates is given by: x = 1/2 (u2 - v2), y=uv, z=z Homework Equations compute the kinetic energy 1/2mv2 in parabolic cylindrical coordinates The Attempt at a Solution Any ideas??

Homework Statement Evaluate \iiint\limits_B e^{x^2 + y^2 + z ^2}dV where B is the unit ball. Homework Equations See above. The Attempt at a Solution Does this evaluate the volume of f(x, y, z) within the unit ball (i.e. anything falling outside the unit ball is discarded)...

Homework Statement I'm trying to express spherical coordinates in terms of cylindrical and vice versa. I would appreciate it if someone could give me some feedback on my attempt at a solution. Thanks for the help! The Attempt at a Solution Spherical(cylindrical) r=(ρ^2+z^2)^(1/2)...

Homework Statement By making two successive simple changes of variables, evaluate: I =\int\int\int x^{2} dxdydz inside the volume of the ellipsoid: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}+\frac{z^{2}}{c^{2}}=R^{2} Homework Equations dxdydz=r^2 Sin(phi) dphi dtheta dr The...

I'm trying to determine the XY coordinates of 3 corner points of a quadrilateral shape based on known lengths of the sides of that shape. I know the lengths of all 4 sides of the shape as well as the lengths of both cross lengths (effectively making two adjacent triangles). I've attached a...

I am trying to understand what generalized coordinates are but I'm having some trouble. After reading up on them a bit my best understanding of the idea of generalized coordinates is the following: Because choice of coordinate system is arbitrary when solving physical systems (or anything for...

Hey, Whenever I read Relativity I get stuck around Gaussian coordinates, i can't seem to find much out about them, do they have another name? does anyone know any good resources explaining them? or am I just in over my head? thanks guys,

Hi, I have a pretty simple question but I'm not certain I know how to phrase it properly. I will try. When we are integrating using cartesian coordinates to find the area under a curve, area under the x-axis is negative and area above the x-axis is positive. This makes sense when I...

Homework Statement The x-y coordinates are being transformed into the u-v coordinates. Based on the diagram, u lies along x while v makes an angle α with x.The Attempt at a Solution The answer defined u and v weirdly.. Shouldn't x = u and y = v sin α ??

Hey everyone, I cannot seem to figure this out and I'm having a hard time finding any guides online for this stuff. All I can find are calculators. I was wondering if it would be possible to calculate my Geographic Coordinates on Earth if I had the Horizontal and Celestial coordinates of a...

Homework Statement https://dl.dropbox.com/u/64325990/cylindrical.PNG The Attempt at a Solution Okay so I found r = 2.24 and z = -3. However I am stuck at finding theta. I think I just don't understand what the question means when it says "In addition, the line defined by theta = 0 in...

I'm not sure what's going on in outgoing Eddington-Finkelstein coordinates for a Schwarzschild black hole. Future-directed timelike curves can be followed from inside the event horizon to outside it (page 185/186 of Sean Carroll's online GR notes...

Hi I have an orthogonalized rotation matrix -0.500000 -0.866025 0.000000 0.866025 -0.500000 0.000000 0.000000 0.000000 1.000000 for the following unit cell: a b c alpha beta gamma space group 131.760 131.760 120.910...

When plotting graphs in polar coordinates, how does one know when to make the graph sharp (at θ=0) (as in for the graph for r=1-cosθ) as opposed to a dimple (r=3/2 + cos θ) ?

It's a standard fact of GR that at a given point in space-time, we can construct a coordinate system such that the metric tensor takes the form of Minkowski spacetime and its first derivatives vanish. Equivalently, we can make the Christoffel symbols vanish at point. Moreover, the fact that, in...

Homework Statement Integrate y/(x^2+y^2) for x^2+y^2<1 and y> 1/2 ; use change of variables to polar coordinates Homework Equations THe above The Attempt at a Solution the variables transform as y=rsinz x=rcosz, where z is an angle between pi/6 and 5*pi/6 = which is the...

Homework Statement I'm not grasping how to convert a surface with known rectangular graph to a parametric surface (using some polar techniques, I assume). I would appreciate it if someone could clarify the conversion process. One of the examples is as follows: A sphere...

Hello Folks, I have this equation to solve (expressed in LaTeX): \frac{\partial{h}}{\partial t} = \frac{1}{n} \left[ \frac{1}{r^2 \sin^2{\phi}} \frac{\partial}{\partial \theta} \left( K \frac{\partial h}{\partial \theta} \right) + \frac{1}{r^2 \sin \phi} \frac{\partial}{\partial \phi}...

Hey all, I've never taken a formal class on tensor analysis, but I've been trying to learn a few things about it. I was looking at the metric tensor in curvilinear coordinates. This Wikipedia article claims that you can formulate a dot product in curvilinear coordinates through the following...

Hi, I am learning about Polar Coordinates and how they can be written in several equivalent ways. I understand how you can add 360 to angles and use negative angles to represent the same point. However, I have a very hard time understanding how you can write the same point but with a...

i am a chemical engineer but this is fluid mechanics stuff so i figured you physics geniuses would know this stuff so to find the z component of force exerted by fluid on the surface of the sphere they find the normal force acting on a surface element of the sphere, integrated over the entire...

I need to transform cartesian coordinates to spherical ones for Minkowski metric. Taking: (x0, x1, x2, x3) = (t, r, α, β) And than write down all Christoffel symbols for it. I really have no clue, but from other examples I've seen i should use chain rule in first and symmetry of...

How to express electromagnetic field tensor in curvilinear coordinates, that is given a curvilinear coordinates (t,\alpha,\beta,\gamma) with metric tensor as follows: n_{\mu \nu }= \left[ \begin{array}{cccc}h_0^2& 0 & 0 & 0 \\ 0 & -h_1^2 & 0 & 0 \\ 0 & 0 & -h_2^2 & 0 \\ 0 & 0 & 0 & -h_3^2...

Hi all, In flat space-time the metric is ds^2=-dt^2+dr^2+r^2\Omega^2 The Schwarzschild metric is ds^2=-(1-\frac{2MG}{r})dt^2+\frac{dr^2}{(1-\frac{2MG}{r})}+r^2d\Omega^2 Very far from the planet, assuming it is symmetrical and non-spinning, the Schwarzschild metric reduces to the...

Hey! I was reading Goldestein's book on classical mechanics and I came across this (Page 20 3rd Edition): "Note that in a system of Cartesian coordinates the partial derivative of T with respect to qj vanishes. Thus, speaking in the language of differential geometry, this term arises...

Hello everyone! I'm new on the forum (been browsing threads for some time though) and this post is both an introduction of myself and a first question. I have a huge interest for physics but my working knowledge (having studied it in school, oh well some 15 years ago) is limited to classical...

In some texts about Lagrangian mechanics,its written that the generalized coordinates need not be length and angles(as is usual in coordinate systems)but they also can be quantities with other dimensions,say,energy,length^2 or even dimensionless. I want to know how will be the Lagrange's...

Homework Statement Sketch the curve r = 1 + 2cosθ in polar coordinates. Homework Equations None that I can think of, it's graphing. The Attempt at a Solution What I was trying to was use the method of finding cartesian coordinates and plugging different values of θ into the equation to...

Guys, I read that integrating the ds gives the arc length along the curved manifold. So in this case, I have a unit sphere and its metric is ds^2=dθ^2+sin(θ)^2*dψ^2. So how to integrate it? What is the solution for S? Note, it also is known as ds^2=dΩ^2 Thanks!

Proof -- Express in Clyndrical Coordinates Homework Statement Show that when you express ds^2 = dx^2 + dy^2 +dz^2 in cylindrical coordinates, you get ds^2 = dr^2 + r^2d^2 + dz^2. Homework Equations x=rcosθ y=rsinθ z=z The Attempt at a Solution EDIT// I was really over thinking...

Homework Statement Find limits of integration for volume of upside down cone with vertex on origin and base at z=1/sqrt(2). Angle at vertex is pi/2. Do this in cylindrical coordinates. Homework Equations None. The Attempt at a Solution My inner integral conflicts with the books...

Hi! I was just wondering if anyone knows where I can find a software/algorithm that can give me the postion of the sun and the moon in ECEF coordinates? If not, do you have any clues to how I might start building one? I am an engeneering student, so I don't have a lot of knowlegde about...