Coordinates Definition and 1000 Threads

I'm reading Leonard Susskind's The Theoretical Minimum Vol. 1. 1. The problem: I'm on the section in which he asks the readers to derive the Lagrangian for a particle on a rotating carousel in polar coordinates. 2. Relevant ideas: The same Lagrangian in Cartesian coordinates is given as...

Alright, so I was reading up on tensors and such with non-Cartesian coordinate systems all day but now I'm a bit tired an confused so you'll have to forgive me if it's a stupid question. So to express the dot product in some coordinate system, it's: g(\vec{A}\,,\vec{B})=A^aB^bg_{ab} And, if...

I'm rather new here so please forgive me if this is answered somewhere else, but I was unable to find it while searching around. For some calculations I'm looking to perform I need to know the geocentric equatorial coordinates of the sun on a given date. However, the only place I know they...

Homework Statement Find the Volume of the solid that the cylinder ##r = acos\theta## cuts out of the sphere of radius a centered at the origin.Homework Equations The Attempt at a Solution I have defined the polar region as follows, $$D = \{ (r,\theta) | -\pi/2 ≤ \theta ≤ \pi/2 , 0 ≤ r...

When you have a general coordinate chart on spacetime you have a lot of freedom to pick your coordinates, but you are always going to have 4 coordinates and each 4-tuple uniquely (in that chart) identifies one event in the manifold. When you are choosing generalized coordinates for a...

Homework Statement Hi! This is not really a problem. I'm just confused on how to express the charge distribution of a set of point charges in spherical coordinates. From our discussion, ρ(\vec{r})=\sum\limits_{i=1}^N q_i δ(\vec{r}-\vec{r}') where \vec{r} is the position of the point where...

Homework Statement In spherical coordinates (ρ,θ,ø); I understood the ranges of ρ, and θ. But ø, still eludes my understanding. Why is ø only from 0 to π, why not 0 to 2π??

What am I doing wrong? Convert $$r = 2sin\theta$$ to an equation in rectangular coordinates.. $$x^2 +y^2 = r^2$$ $$x^2 + y^2 = 2y$$ $$x^2 + y^2 - 2y = 0$$ $$x^2 + y^2 - 2y - 1 = 1$$ $$x^2 + (y-1)^2 = 1$$ Coordinates are $$(0,1)$$ yes?

Hello, I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: 2W = σijεij Where σ and ε are symmetric rank 2 tensors. For cartesian coordinates it is really easy because the metric is just the identity matrix, hence: 2W = σxxεxx +...

Dear kind helpers, actually I am not 100% sure whether this is the right place to post, as it is not a homework in the sense of an exercise sheet. But I think it could be because it feels pretty basic and that I should be able to solve it. Though I really searched for a solution but could not...

Hi all. I'm working on a project that requires me to perform calculations in Fermi normal coordinates to certain orders, mostly 2nd order in the distance along the central worldline orthogonal space-like geodesics. In particular I need a rotating tetrad propagated along the central worldline...

If you rotate your rectangular coordinate system (x,y) so that the rotated x'-axis is parallel to a vector (a,b), in terms of the (x,y) why is it given by x'=ax+by y'=bx-ay I got x'=ay-bx, y'=by+ax from y=(b/a)x. By the way this is from solving the PDE aux+buy=0 by making one of the...

Hi, I'm working on a project that would take a 3d image using stereocopic camera and would record the depth and the 2d (x1,y1) , (x2,y2) coordinates of a single point in the image. The depth is found using the focal point, disparity, and the distance between the difference the camera sees on...

Dear all, As I was reading my book. It said that the line element of a particular coordinate system (spherical) in R^{3} is so and so. Then it said that the metric is flat. I don't get how the metric is flat in spherical coordinate. Could someone shed some light on this please? Thanks

I just derived the 3-D Cristoffel symbol of the 2nd kind for spherical coordinates. I don't think I made any careless mistakes, but once again, I just want to verify that I am correct and I can't find any place on line that will give me the components of the symbol so I can check myself. Here...

I recently derived a matrix which I believe to be the metric tensor in spherical polar coordinates in 3-D. Here were the components of the tensor that I derived. I will show my work afterwards: g11 = sin2(ø) + cos2(θ) g12 = -rsin(θ)cos(θ) g13 = rsin(ø)cos(ø) g21 = -rsin(θ)cos(θ)...

I am setting up a numerical simulation from a 2D discretization of the heat equation in cylindrical coordinates. my spatial variables are radius (r), height (z), and azimuth (ø). The assumption is that there is no gradient along the azimuth direction (if temperature is T then dT/dø = 0)...

hi fellas, i have been given a graph from which i can extract the coordinates and the slopes but all i need is to generate the function this graph represents. can you suggest me any manual procedure to do this mathematically or do i have to use software to generate polynomial functions? if...

So I'm wondering, should I use Cartesian or Polar Coordinates to store intergalactic objects in DB? I'm currently prototyping a game idea that can be oversimplified as a spaceship simulator in infinite space. I'm considering grouping objects together so that they have a "parent super-space"...

Lim (x, y)->(0,0)(X^3+y^3)/(x^2+y^2) The answer is -1, but I can't get it there. Here is what I did. ((Rcosx)^3 +(rsinx)^3)/((rcosx)^2+(rsinx)^2) Then by factoring out a r squared from top and bottom I'm left with a denominator of (sin^2(x ) + cos^2 (x)) which simplifies to 1. And a numerator...

The conic equation has 2 versions in cartesian coordinates: The general: ##Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0## And the parametric: ##y^2 = 2px + (e^2-1)x^2## In polar coordinates, I known just the parametric: ##r = \frac{p}{1+e\cos(\theta)}## But exist a general form too?

Homework Statement The points O,A and B are vertices of an equilateral triangle. Find a and b O=(0,0) A=(a,11) B=(b,37) Homework Equations ##c^2=a^2+b^2## The Attempt at a Solution Let AB =c Then ##c=\sqrt{(a-b)^2+(11-37)^2}=\sqrt{(a-b)^2+676}## Since it is an equilateral triangle...

Three unit circles $C_1$, $C_2$ and $C_3$ in a plane have the property that each circle passes through the centres of the other two. A square $ABCD$ surrounds the three circles in such a way that each of its four sides is tangent to at least one of $C_1$,$C_2$ and $C_3$. $A=(0,0)$, $B=(a,0)$...

Hello everyone ,i have captured car positons at differents frames.http://www.imagesup.net/pt-7140205392313.png%5D%5BIMG%5Dhttp://www.imagesup.net/dt-7140205392313.png Suppose car's(left side car which is coming towards us) centroid is at video frame1 is P(x1,y1) and Q(x2,y2) at video frame4...

Hello! :) From the relations: $$\partial_{r}=\cos \theta \cdot \partial_{x}+ \sin \theta \cdot \partial_y$$ $$\partial_{\theta}=-r \sin \theta \cdot \partial_x+ r \cos \theta \cdot \partial_y$$ we get: $$\partial_y=\sin \theta \cdot \partial{r}+\frac{\cos \theta}{r} \cdot \partial_{...

Homework Statement Homework Equations Possions Equation and boundary conditions... The Attempt at a Solution First Part that I think is right... However when I try and apply the boundary conditions ie V(a)=V(r)=0... I can't get the answer! And for the last...

Homework Statement Need a free program to plot expressions in polar coordinates. For example, I want to plot the equipotentials for an expression in polar coordinates of the potential for a dipole charge, 4q and -q separated by a distance L. Homework Equations V=kq(4/r1 - 1/r), where r12...

Homework Statement For a set of vectors in R3, is the set of vectors all of whose coordinates are integers a subspace?The Attempt at a Solution I do not exactly understand if I should be looking for a violation or a universal proof. If x,y, z \in Z then x,y,z can be writted as...

Homework Statement A particle moves with const speed v along the curve r(θ) = a(1+cos θ). Starting with the general expression for the velocity vector v in polar coordinates solve for θ_dot in terms of v, k, and θ. What does the sign of θ_dot signify?Homework Equations v = r_dot*r_hat +...

given that x'=f(x,y) y'=g(x,y) iff the vector function (r, θ) is a sloution of the system r'=f(rcosθ,rsinθ)cosθ +g(rcosθ,rsinθ)sinθ am trying to show that this is true but i just don't get where the sinθ and cosθ come from, how do i get to that

I'm confused why when using cylindrical coordinates three unit vectors are needed. My book says that the three unit vectors are one for the radial direction which is bound to the xy plane and then a unit vector in the z direction. It goes on to say that there is another unit vector associated...

Hi everyone, Here's the problem I have. Given two unit vectors A, B and angle φ between them. Find the coordinates (in 3D) of a unit vector C so that the angles between C and A,B be α and β respectively. α + β => φ and α + β + φ <= 360° It looks trivial to me and yet here I am asking for...

In a problem that requires converting from cartesian to polar coordinates, I need to take \frac{dr}{dx}. I tried doing it two different ways but getting two completely different answers.. Method 1: r=\sqrt{x^2+y^2} \frac{dr}{dx}=\frac{1}{2}\frac{1}{\sqrt{x^2+y^2}}2x \;\; =...

Homework Statement ∫∫Rarctan(y/x) dA, where R={(x,y) | 1\leqx2+y2\leq4, 0\leqy\leqx Homework Equations x=rcos(θ) y=rsin(θ) x2+y2=r2 The Attempt at a Solution I know that the range of r is 1 to 2 but I can't figure out how to change the second part into θ. If I change y and x to...

1. . An electric dipole located at the origin in free space has a moment p = 3ax −2ay +az nC·m. Find V at r = 2.5, θ =30◦, φ =40◦. I find it difficult to solve when its in spherical co-ordinates.2.Relevent Eq V =P.(r-r')/( 4∏ε|r−r'|2)(|r-r'|)I am confused how to find a unit vector on spherical...

Hey pf! I was thinking about how div(curl(f)) = 0 for any vector field f. However, is this true for div and curl in spherical coordinates? It doesn't seem to be. If not, what needs to happen for this to be true in spherical coordinates?? Thanks all!

Homework Statement Write a triple integral in spherical coordinates that represents the volume of the part of the sphere X^2+Y^2+Z^2=16 that lies in the first octant(where x,y, and z are coordinates are all greater than or equal to zero) Homework Equations So i know this is in...

Given Cartesian (x,y,z), Spherical (r,\theta,\phi) and parabolic (\varepsilon , \eta , \phi ), where \varepsilon = r + z = r(1 + \cos(\theta)) \\\eta = r - z = r(1 - \cos( \theta ) ) \\ \phi = \phi why is it obvious, looking at the pictures [SIZE="1"](Is my picture right or is...

The position vector ##\vec{r}## in cartesian coordinates is: ##\vec{r} = x \hat{x} + y \hat{y}##, in polar coordinates is: ##\vec{r} = r \hat{r}##. But, given a curve s in somewhere of plane, with tangent unit vector ##\hat{t}## and normal unit vector ##\hat{n}## along of s, exist a definition...

Dear Math and Physics fans You have always been so helpful in the past and I was hoping that I could call on your expertise once again. I want to make a wedge filter in MATLAB so I can determine the orientation of the ellipse of a centered 2D fft. I tried to make an new image where...

Homework Statement I have a function y that is axisymmetric, so that y=y(r). I want to solve for r such that ∇2y(r) = Z. Can anyone tell me if I'm following the right procedure? I'm not sure since there are two "∂/∂r"s present... Homework Equations ∇2 = (1/r)(∂/∂r)(r*(∂/∂r)) +...

the coordinates of cycloide are ##x= a (\theta- sin \theta)## ##y= a(cos \theta -1)## If i use ##\theta =\omega t## this is a example of cycloid but, if i use ##\theta=\cos (\omega t)##, ¿this is a cycloid? My teacher says that in a cycloid pendulum ##\theta## must be oscillatory...

Marla is running clockwise around a circular track. She runs at a constant speed of 3 meters per second. She takes 46 seconds to complete one lap of the track. From her starting point, it takes her 12 seconds to reach the northernmost point of the track. Impose a coordinate system with the...

I am finding the electric field from a spherical shell at a point on the z-axis outside the shell. The shell is centered at the origin,and I am only allowed to use coulomb's law. I want to find dE in spherical coordinates first then transform it to Cartesian before integrating to get E. So I...

Homework Statement hi,guys. The directions of shooting e=cos\alphacos\varphii+cos\alphasin\varphij+sin\alphak 0<\varphi<=2π;\varphi -horizontally \alpha[0,π];\alpha is vertically initial speed=v0 I need to calculate the surface equation of canon shots (where it hits). In other words equations...

Homework Statement Let V be the volume of the solid enclosed by the sphere x^2 + y^2 + z^2 - 2z = 0 , and the hemisphere x^2 + y^2 + z^2 = 9 , z ≥ 0. Find VHomework Equations Using spherical coordinates: x^2 + y^2 + z^2 = ρ^2 z = ρcos(ø) The Attempt at a Solution So I changed both of them to...

Polar Coordinates --- Graphing the points of when theta<0 Hi everyone, I'm working with an online graphing program desmos.com. It's great, and actually tons of fun. I'm currently working with polar coordinates but the only flaw of this grapher is that when working with polar coordinates...

I've got a Green's function in which all the impulses are on the line from the north pole to the origin (polar angle θ=0) and terminating with a point impulse at the north pole. I've found its gradient at a field point, and I want to rotate everything to a new coordinate system with the source...

Homework Statement Use cylindrical coordinates to find the volume of the solid that the cylinder r = 3cos/theta cuts out of the sphere of radius 3 centered at the origin. Homework Equations Why do we evaluate theta from 0 to pi instead of from 0 to 2pi? Don't we want to go all the...

1. Homework Statement [/b] Suppose the lim(x,y) →(0,0) (xy)/SQRT[x^2 + y^2] if it exists find the limit. The Attempt at a Solution x = rcosΘ y = r sinΘ r = SQRT[x^2 + y^2] ∴ lim[SUB]r → 0 (r2cosΘrsinΘ)/ r = rcosΘsinΘ \leq r and so -r \leq(xy)/SQRT[x^2 + y^2] \leq r ... ... I can...