Coordinates Definition and 1000 Threads

Homework Statement Find the shortest distance between two points using polar coordinates, ie, using them as a line element: ds^2 = dr^2 + r^2 dθ^2Homework Equations For an integral I = ∫f Euler-Lagrange Eq must hold df/dθ - d/dr(df/dθ') = 0 The Attempt at a Solution f = ds = √(1 + (r *...

Homework Statement Using calculus, find the coordinates of the point on the line y =-2x+5, which is closest to the origin, and the corresponding value of D Homework Equations y = -2x +5 The Attempt at a Solution I know I need to find a line that is perpendicular to the line of...

I want to verify: \vec A=\hat R \frac{k}{R^2}\;\hbox{ where k is a constant.} \nabla\cdot\vec A=\frac{1}{R^2}\frac{\partial (R^2A_R)}{\partial R}+\frac{1}{R\sin\theta}\frac{\partial (A_{\theta}\sin\theta)}{\partial \theta}+\frac{1}{R\sin\theta}\frac{\partial A_{\phi}}{\partial \phi}...

Homework Statement What is the compensation factor for converting dy dx to cylindrical coordinates? Homework Equations None that I know of besides the bottom ones as part of the attempt The Attempt at a Solution So I know that the conversion formulas for going from Cartesian (x,y,z)...

Homework Statement Calculate the moment of inertia of a uniformly distributed sphere about an axis through its center. Homework Equations I know that $$I= \frac{2}{5} M R^{2},$$ where ##M## is the mass and ##R## is the radius of the sphere. However, for some reason, when I do this...

http://en.wikipedia.org/wiki/Gradient#Cylindrical_and_spherical_coordinates which formula do we apply to get the gradient in spherical coordinates?

Homework Statement I have a graph 1/x^2=y^2+z^2 where z=rsin(θ) and y=rcos(θ) where 0≤r≤1 and 0≤θ≤2∏ on the zy-plane The end result is attached (sorry, I'm not aware of how to use Latex :[ ) I can kind of understand how they determined the first bounds for the integral: the lowest x...

Hi, I have a data set containing values for power and direction. I would like to produce a probability density estimate. The data can have multiple sources so I want to use a nonparametric method. I work in python which has a method for kernal density estimation (KDE), which I think should be...

hi all, attached here is my code for 2d fdtd in polar coordinates, from 'numerical electromagnetic: the fdtd method (umran s inan, pg 94-96) written in fortran90. I have try a few approach I could think about to troubleshoot this code but the output is still infinity. Anybody here can give me...

I am trying to read into quantum mechanics and am reading a lot of rules that do not cite evidence and while it is probably just the books I am reading, I was wondering if anyone could post some links to experiments that verify some of this. First of all, this book "Quantum Mechanics -...

Hi Say I have a point on a unit sphere, given by the spherical coordinate $(r=1, \theta, \phi)$. Is this point equivalent to the point that one can obtain by $(x,y,z)=(1,0,0)$ around the $y$-axis by an angle $\pi/2-\theta$ and around the $z$-axis by the angle $\phi$? I'm not sure this is...

Here is the question: Consider the differential equation $$x' = a_1 x + a_2 x^2 + a_3 x^3 + \cdots,$$ with $a_1 \neq 0$. Show that there exists a $C^2$ change of coordinates of the form $x = y + \alpha y^2$ that rewrites the equation (locally around $x=0$) as $$y' = a_1 y + b_3 y^3 +...

Homework Statement Use polar coordinates to find the volume of the solid bounded by the paraboloid z = 47 - 5x2 - 5y2 and the plane z = 2. Homework Equations x2 + y2 = r2 x = rcosθ y = rsinθ The Attempt at a Solution I substituted the z = 2 into the equation given, 2 = 47 -...

Homework Statement Let C be a curve given by y = f(x). Let K be the curvature (K \ne 0) and let z = \frac{1+ f'(x_0)^2}{f''(x_0)}. Show that the coordinates ( \alpha , \beta ) of the center of curvature at P are ( \alpha , \beta ) = (x_0 -f'(x_0)z , y_0 + z) Homework Equations The...

Find the area of the following region: Inside: r2 = 6 cos 2θ Outside: r = √3 Here's how I've set up the integral. I have to be making a mistake somewhere in the set up, but I can't figure it out. r1 = √3 r2 = (\sqrt{6 cos 2θ}) \frac{Area}{4}= \frac{1}{2}\int\ (\sqrt{6 cos 2θ})^{2}...

There is a technical distinction between a vector and the coordinates of a vector. Are projective (also called "affine") coordinates the coordinates of vectors? I'm thinking of how translation is accomplished by matrix multiplication. For example the point (x,y) in 2-D is given coordinates...

Homework Statement Hello, I posted a similar question in the physics section but no one was able to help, I am first going to include a link to the older problem where I was attempting to find the ,(Finding the local flat space of the Poincare half disk metric), and explain what is different...

Hello. I don't know how to prove that a certain function is a solution to the scalar wave equation in cylindrical coordinates. The scalar wave equation is \left(\nabla^2+k^2\right)\,\phi(\vec{r})=0,which in cylindrical coordinates is...

So, I'm to show that in spherical coordinates, the length of a given path on a sphere of radius R is given by: L= R\int_{\theta_1}^{\theta_2} \sqrt{1+\sin^2(\theta) \phi'^2(\theta)}d\theta, where it is assumed \phi(\theta), and start coordinates are (\theta_1,\phi_1) and (\theta_2, \phi_2)...

I want to transform from rectangular coordinates ( xyz) to (x",y",z") rectangular coordinates that is rotated at the origin as show in the attachment. Then I want to transform (x",y",z") rectangular coordinates into Spherical coordinates. Attach is the method I use, I want to verify I am doing...

Hello, my best problem is about find the integration limits. in cylindrical coordinates- where V is limited by the cylinder y^2+z^2=9 and the planes x = 0, y = 3x and z = 0 in the first octant.

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Given a specific metric, is there a easy way to transform it in Synchronous coordinates? For example having dsigma2 = (1+z)^2 dt^2 - ds^2 - s^2 dphi^2 - dz^2 , I was able to do some substitutions, but I had to stop at the differential equations presented in the attachement.

I don't have access to Comsol 4.x. I imported a 3D mesh generated from point cloud data and generated a geometry. (A hollow almost-ellipsoid.) I solve my system on the surface/boundary alone; there is no volumetric data. I need to extract 1D data from the surface/boundary at points other...

We start by defining two coordinates ##u=t+r^*## and ##v=t-r^*##. Then we define another two coordinates ##u'=e^{u/4GM}## and ##v'=-e^{-v/4GM}##. But from what I have understood this is true for ##r>2GM##. How do we define ##u'## and ##v'## for ##r<2GM##? I think it's ##u'=e^{u/4GM}## and...

... ... I am curious to know why we have to multiply with e^{-j\omega t} in Fourier transform? What is the purpose of this? I have heard somewhere that the transform is merely a change of variables from one set of coordinates to another. I would like to know more about this. Can you help me?

In polar coordinates we have \vec{r} = r \hat{r} \Rightarrow \vec{v} = \frac{d}{dt}({r \hat{r}}) = \dot{r}\hat{r} + r \frac{d \hat{r}}{dt} . In the book Introduction to Mechanics, K & K says the right term is the component of velocity directed radially outward. (Surely a typo, as the left...

How to translate r = 2 /(2 - cos(theta)) to cartesian coordinates: so far: r = 2 /(2 - cos(theta)) r = 2 /(2 - cos(theta)) |* (2 - cos(theta)) both sides r (2 - cos(theta))= 2 2*r - rcos(theta) = 2 | know x = rcos(theta) 2*r - x...

I know that \oint_{C}\mathrm{d}\vec{l} = 0, for any closed curve C. But when i try to calculate the integral around the unit circle in polar coordinates, I get a result different from zero. Here is my approach : \oint_{C}\mathrm{d}\vec{l} = \int_{0}^{2\pi}\hat{\phi}\mathrm{d}\phi =...

Homework Statement The position of a proton at time t is given by the distance vector \vec{r}(t) = \hat{i}x(t) + \hat{j}y(t) + \hat{k}z(t) A magnetic induction field along the z-axis, \vec{B} = \hat{k}B_{z} exerts a force on the proton \vec{F} = e\vec{v}\times\vec{B} a.) For...

My problem is that I believe I have a wrong concept somewhere, and I can't find what I'm doing wrong exactly. For this problem let's suppose what I want to do is find the rectangular coordinates of BC. I had two "possible solutions" I tried to achieve this, . First the correct one: (I...

I'm currently working out the Schrödinger equation for a proton in a constant magnetic field for a research project, and while computing the Hamiltonian I came across this expression: (\vec{A}\cdot\nabla)\Psi where \Psi is a scalar function of r, theta, and phi. How do you evaluate this...

Hello =] I'm having trouble with this question, can somebody please help me with it! I'll thanks/like your comment if help me =) ![Question][1] I know that for a ellipse the parametric is x=a sin t , b= b cos t t:0 to 2pi (?) for part a) I drew up the graph but not sure if it's...

Homework Statement Find VR_{z}^{2} = \int \!\!\! \int \!\!\! \int_{E} (x^{2} + y^{2})dV given a constant density lying above upper half of x^{2}+y^{2} = 3z^{2} and below x^{2}+y^{2}+z^{2} = 4z.Homework Equations The Attempt at a Solution Why does it say upper half of x^{2}+y^{2} = 3z^{2}? It's...

An industrial tool is made from alaminar material occupyingthe region between thestraight lines y =2, y=1 2x and y =3−x. The density of thematerial varies and is given by thefunction σ(1 + x), where x is the horizontal distancefrom the y-axis and σ is aconstant. The mass of the...

Homework Statement find the area of the surface defined by x2+y2=y, with yE[0,4] The Attempt at a Solution I tried setting it up with cylindrical coordinates, but it doesn't work. Why? ∫40∫2pi0r*dθ*dy, where r=√y Is it because my height, dy, has a vertical direction while its...

Homework Statement Let S be the part of the cylinder of radius 9 centered about z-axis and bounded by y >= 0; z = -17; z = 17. Evaluate \iint xy^2z^2 Homework Equations The Attempt at a Solution So I use the equation x^2 + y^2 \leq 9, meaning that r goes from 0 to 3 Since y...

Hello, let's assume we have an admissible change of coordinates \phi:U\rightarrow \mathbb{R}^n. I would like to know how the inner product on ℝn changes under this transformation. In other words, what is \left\langle \phi (u), \phi (v) \right\rangle for some u,v \in U ? I thought that...

Homework Statement Find polar coordinates. Homework Equations Cartesian: (-3,4) The Attempt at a Solution r = sqrt(9+16) = 5 sinθ = 4/5 cosθ = -3/5 θ = ∏ - arctan(4/3) Answer: (5, ∏ - arctan(4/3)) I do not understand why we have subtracted the value arctan(4/3) from pi?

Hi, I tried using geogebra to find an equation that exactly goes through the list of points I plotted on the graph but I failed to find any way so far. I have tried using, FitExp, FitGrowth, and Fitline, and so far none of them worked. I have no idea what kind of equation this is so I cannot...

Homework Statement Curve C is given in Polar Coordinates by the equation r=2+3sinθ. Consider the usual Cartesian plane and take O as the pole and the positive x-axis as the polar axis. Find points on the curve C where the tangent lines are horizontal or vertical and sketch the curve C...

Jacobi identity in local coordinates?!? Apparently (i.e. according to an article written by physicists), the Jacobi identity for the Poisson bracket associated to a Poisson bivector \pi = \sum\pi^{ij}\partial_i\wedge\partial_j is equivalent to...

Homework Statement Convert the integral from rectangular coordinates to spherical coordinates 2 √(4-x^2) 4 ∫ ∫ ∫ x dz dy dx -2 -√(4-x^2) x^2+y^2 Homework Equations x=ρ sin∅ cosθ y=ρ sin∅ cosθ z=ρ cos∅ In case the above integrals cannot be understood: -2...

Hello how can Convert Cartesian coordinates to spherical with shape? for clear my question i explain a way to convert my coordinates in different spherical. for example i use this diagram to convert Cartesian coordinates to Cylindrical(with image to axises) for example: now how can i do...

Homework Statement I have a path defined in polar coordiantes defined as r=a*cos2(θ). I also have the velocity along this path as a function of θ. I want to find the time take to move between two given angles on the path.2. The attempt at a solution I know that this problem will involve some...

Homework Statement Here is a picture of the situation http://i48.tinypic.com/vnmi5t.jpg Homework Equations polar coordinate system The Attempt at a Solution ok so first I'm attempting to find velocity as a function of time, first I know V=(dR/dt)er +(R)(d∅/dt)e∅ - this is a...

Hellow MHB, I'm trying to understand how can i pass this integral to polar coordinates. My biggest doubt is about the "radius".

In my physics textbook we have d\vec{l}=\hat{z}dz and then it says d\vec{l}\times \hat{R}=\hat{\phi}\sin \left (\theta \right )dz How so? What is \hat{z}\times\hat{R}? If it is \hat{\phi} then where does the sine come from?

Whoops, I figured it out!

Let's start with the motivation - I'm trying to think of ways to talk about building coordinate systems operationally, ideally without directly using ideas like "space like geodesics" that one needs for fermi-normal coordinates. The ideas behind geodesics don't strike me as terribly...