Coordinates Definition and 1000 Threads

I've always been curious why points in polar coordinates are defined as (r,θ) when all equations (including parametric equations formed from them) are defined as r=f(θ). Considering that point in cartesian coordinates are defined as (x,y) where y=f(x). Also a,b=(r,θ) ∫1/2[f(θ)]2 further...

Homework Statement A tourist takes a tour through a city in stages. Each stage consists of 3 segments of length 100 feet, separated by right turns of 60°. Between the last segment of one stage and the first segment of the next stage, the tourist makes a left turn of 60°. At what distance...

Homework Statement Find the area in the polar curve r = sin2θ between 0 and \frac{\pi}{2}. The way to do this is to say the area of a tiny bit of this polar curve, dA = \frac{1}{2}r^{2}dθ so the integral is just \frac{1}{2}\int^{\frac{\pi}{2}}_{0}(sin2θ)^{2}dθ if we did say a function...

I am studying Riemannian Geometry and General Relativity and feel like I don't have enough practice with covariant vectors. I can convert vector components and basis vectors between contravariant and covariant but I can't do anything else with them in the covariant form. I thought converting the...

Homework Statement find the limits on spherical coordinates. where ε is the region between z²=y²+x² and z = 2(x²+y²) no matter what i try i can't seem to find the limits, especially for "ρ", so far i got 0<θ<2Pi and 0<φ<Pi.

Homework Statement Change of coordinates from rectangular (x,y) to polar (r,θ). Not sure what's wrong with my working.. Homework Equations The Attempt at a Solution

Spherical, Cylindrical or Polar Coordinates Homework Statement I have attached an image of the problem. I know that the solution is number 1 but I'm having some difficulty understanding why. In solution one is it using cylindrical coordinates> My first response to this question had been to...

Homework Statement given I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ the bounds of the integrals: left most integral: from 0 to pi middle integral: from 0 to pi/2 right most integral: from 1 to 3 i have no idea how to graph this, i was hoping someone would be able to recommend some techniques.

Homework Statement Consider the interated integral I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ -the bounds of the first integral (from left to right) are from 0 to pi -the bounds of the second integral are from 0 to pi/2 -the bounds of the third integral are from 1 to 3 a)express I as an interated...

let us denote the joint eigenstate of \hat{L^{2}}and \hat{L_{z}} by ll,m> and we know that if we are in spherical coordinates, \hat{L^{2}} and \hat{L_{z}} depend on θ and ∅, so we denote the joint eigenstate by: <θ∅l l,m>.. why?

There has been a few times when I switch from Cartesian to cylindrical coordinates to integrate I would get the wrong because I used the wrong substitution. For instance I would use x = rcos(θ) and y = rsin(θ) where r and θ are variable when I was suppose to leave r as a constant. Question...

Homework Statement I don't have a specific problem in mind, it's more that I forgot how to solve the particular equation from first principles. \nabla^{2} \Phi = k^{2}\Phi Places I've looked so far have just quoted the results but I would like the complete method or the appropriate...

questioning what ρ does. What is the difference between the two equations? Let k be the angle from the positive z-axis and w be the angle from the pos x-axis parametric equation of a sphere with radius a paramet eq. 1: x = asin(k)cos(w) y = asin(k)sin(w) z= acos(k) 0≤w≤2pi 0≤k≤pi...

My question is kinda simple but it has been causing me some trouble for a while. In the problem of the pendulum rotating about an axis, why isn't the angle of rotation about the axis a generalized coordinate? The doubt appears when i try to write the hamiltonian for the system and i don't know...

Homework Statement Calculate the deformation of a sphere of radius R and density \rho under the influence of its own gravity. Assume Hooke's law holds for the material. Homework Equations Not applicable; my question is simply one of understanding. The Attempt at a Solution I want...

Continued from; Originally Posted by Jameson http://www.mathhelpboards.com/f2/understanding-how-deal-fractions-using-brackets-2596/#post11674 What is the full problem you are trying to solve? I can't make sense of your post until I know that. I have a circle problem and am trying to find...

It seems that acceleration at some point in Rindler coordinates completely determines it's distance from rindler horizon, right? If we have two rockets with equal hight and experiencing equal acceleration at the bottom there are no other parameters we can vary to get different results for two...

Homework Statement Take the double integration of http://webwork.usi.edu/webwork2_files/tmp/equations/08/1294e87299342c0ccfe2f8a97055da1.png when f(x)=sqrt(4x-x^2) Homework Equations x=rcos(theta) y=rsin(theta) The Attempt at a Solution I know I plug in the r*cos(theta) and...

Homework Statement Consider the complex function f (z) = (1 + i)^z with z ε ℂ. 1. Express f in polar coordinates. Homework Equations The main derived equations are in the following section, there is no 'special rule' that I (to my knowledge) need to apply here. The Attempt at a...

∫03∫0sqrt(9-x2)∫sqrt(x2+y2)sqrt(18-x2-y2) (x2+y2+z2)dzdxdy x=\rhosin\varphicosθ y=\rhosin\varphisinθ z=\rhocos\varphi Change the integrand to \rho and integrate wrt d\rhodθd\varphi I don't know how to find the limits of integration. Normally I would draw a picture and reason it out...

In spherical coordinates we have three axes namely r, θ, ∅ the ranges of these axes are 0≤r≤∞ 0≤θ≤∏ 0≤∅≤2∏ what will happen in a physical situation if we allow θ to change from zero to 2∏

Hello all, I've been going through Bernard Schutz's A First Course In General Relativity, On Chapter 5 questions atm. Should the Christoffel Symbols for a coordinate system (say polar) be the same for vectors and one-forms in that coordinate system? I would have thought yes, but If you...

My class is starting to cover E&M in Lorentz covariant form, and obviously the subject of tensors came up. The problem is that my prof defines tensors in terms of coordinates, which is ugly and against the spirit of relativity. Is there a way of doing tensors coordinate-free in a physics...

Homework Statement I'm trying to get to grips with Godel's 1949 Paper on Closed Time-like Curves (CTCs). Currently I'm trying to confirm his transformation to cylindrical coordinates using maple but seem to keep getting the wrong answer. Homework Equations The line element in cartesian...

The coordinate speed of light relative to its speed at infinity is calculated as (1-2M/r)c (at infinity) yes?? SO it makes sense that local measurements made with local rulers and clocks which are contracted and dilated respectively would still be c for radial measurements. But how does that...

The question is in the paint document I wanted to know why they integrated from 0 to pi and not from 0 to 2pi

Hello, I am struggling with what was supposed to be the simplest calc problem in spherical coordinates. I am trying to fid the center of mass of a solid hemisphere with a constant density, and I get a weird result. First, I compute the mass, then apply the center of mass formula. I divide...

Homework Statement The problem is to calculate the volume of the region contained within a sphere and outside a cone in spherical coordinates. Sphere: x2+y2+z2=16 Cone: z=4-√(x2+y2) Homework Equations I am having difficulty converting the equation of the cone into spherical coordinates...

Homework Statement Homework Equations All above. The Attempt at a Solution Tried the first few, couldn't get them to work. Any ideas, hopefully for each step?

Homework Statement Use spherical coordinates. Evaluate\int\int\int_{E}(x^{2}+y^{2}) dV where E lies between the spheres x2 + y2 + z2 = 9 and x2 + y2 + z2 = 25. The attempt at a solution I think my problem may be with my boundaries. From the given equations, I work them out to be...

Hello! I seem to have a problem with spherical coordinates (they don't like me sadly) and I will try to explain it here. I need to calculate a scalar product of two vectors \vec{x},\vec{y} from real 3d Euclidean space. If we make the standard coordinate change to spherical coordinates we can...

Homework Statement Integrate: \displaystyle f\left( x,y \right)=\frac{{{x}^{2}}}{{{x}^{2}}+{{y}^{2}}} on the region: \displaystyle D=\left\{ \left( x,y \right)\in {{\mathbb{R}}^{2}}:0\le x\le 1,{{x}^{2}}\le y\le 2-{{x}^{2}} \right\} TIP: Use change of coordinates: \displaystyle...

Homework Statement Let W= {(x,y,z)| x^2 + y^2 ≤ 1, -1 ≤ z ≤ 1} (W is a bounded cylindrical region) Evaluate the triple integral f(x,y,z)= z^2 x^2 + z^2 y^2 over W. Use cylindrical coordinates Homework Equations i don't see any relevant equations besides the obvious cylindrical...

Not much else to say other than the title. In the Schwarzschild spacetime, the radial coordinate r didn't represent radial distance, but it at least represented the thing that determines the area of a sphere centered on the large mass. It doesn't seem like that interpretation can be given to the...

Laplace axisymmetric $u(a,\theta) = f(\theta)$ and $u(b,\theta) = 0$ where $a<\theta<b$. The general soln is $$ u(r,\theta) = \sum_{n=0}^{\infty}A_n r^n P_n(\cos\theta) + B_n\frac{1}{r^{n+1}}P_n(\cos\theta) $$ I am supposed to obtain $$ u(r,\theta) = \sum_{n =...

More and more my teacher has talked about how results for mechanical problems are the same no matter what our coordinate system is (though it may be easier to calculate them in some coordinate frames). I must however admit, that I have never really had a clear explanation of what it means to do...

Homework Statement Hi The expression for the magnetic field from an infinite wire is \boldsymbol B(r) = \frac{\mu_0I}{2\pi}\frac{1}{r} \hat\phi which points along \phi. I am trying to convert this into cartesian coordinates, and what I get is \boldsymbol B(x, y) =...

Hi guys, i need help for homework, it seems easy, but i can't do it:cry:, no calculation to do only writing 2D coordinates in different frames. Homework Statement The hallmark of an inertial frame is that any object which is subject to zero net force will travel in a straight line in a...

Homework Statement Let A,B,C be three sets of complex numbers as defined below A = {z:|z+1|\leq2+Re(z)}, B = {z:|z-1|\geq1} and C=\left\{z: \frac{|z-1|}{|z+1|}\geq 1 \right\} The number of point(s) having integral coordinates in the region A \cap B \cap C is Homework Equations...

1. I basicly have to find the coordinates of P. All the pink lines are know, coordinates of points A and centre of circle are know. 2. (x-a)^2 + (y-b)^2 = r^2 [b]3. I try to substitute mx+c into the equation and get (x-a)^2 + (y-mx-c)^2 + r^2= 0 but I can't work out what m and c...

Homework Statement Using polar coordinates, show that lim (x,y)->(0,0) [sin(x^2+y^2)]/[x^2+y^2] = 1 Homework Equations r^2=x^2+y^2 The Attempt at a Solution I was able to get the limit into polar coordinates: lim r->0^+ [sin(r^2)]/r^2 but I'm not sure how to take this limit. I tried...

Hi everyone. I am a little desperated cause my exam is on monday and still much stuff to do. I don't get when I am supposed to use/consider radial and tranversal forces. Most excercises say "it rotates on the horizontal or vertical" I guess this is the info that tells me if there is...

I have never solved an equation in polar form. I am not sure with how to start. Solve Laplace's equation on a circular disk of radius a subject to the piecewise boundary condition $$ u(a,\theta) = \begin{cases} 1, & \frac{\pi}{2} - \epsilon < \theta < \frac{\pi}{2} + \epsilon\\ 0, &...

Homework Statement An equation is given in spherical coordinates. Express the equation in rectangular coordinates. r2cos2∅=z So first thing I did was used a half angle formula r2 (cos2∅-sin2∅=z Now, I'm stuck. The answer is x2-y2=z Guidance is appreciated (: Homework...

First post here in PF, so forgive me if this question is in the wrong place. I'm a student in computational plasma physics. The code I work with utilizes magnetic field aligned coordinates, and as a necessity, it is sometimes useful to convert between spatially regular coordinates (cartesian...

Homework Statement The concrete slab supports the six vertical loads shown. Determine the x- and y-coordinates of the point on the slab through with the resultant of the loading system passes. Image attached Homework Equations The Attempt at a Solution I started off by...

Homework Statement Hi, I'm trying to find the area of a circle in polar coordinates.I'm doing it this way because I have to put this into an excel sheet to have a matrix of areas of multiple circles. Here is an example of the problem. a= radius of small circle (gamma, r0) = polar coordinate...

Hi everyone, Defined the Fermi Normal Coordinates (which can be seen for example http://relativity.livingreviews.org/open?pubNo=lrr-2011-7&amp;page=articlese10.html" ) is there any heuristic argument to explain why the area element is something proportional to the element of solid angle? I...

Homework Statement I need to isolate the expressions for ellipsoidal coordinates (see below)... I'm given: x2=\frac{(a^2+\lambda)(a^2+\mu)(a^2+\nu)}{(a^2-b^2)(a^2-c^2)} y2=\frac{(b^2+\lambda)(b^2+\mu)(b^2+\nu)}{(b^2-a^2)(b^2-c^2)}...

Say a person is positioned here: 40.23°N and 15.89°E and was examining the night sky. How do you calculate the declination and Right Ascension from that location's coordinates? I know the RA is measured in hours up to 24 and Declination in degrees. Any ideas?