Coordinate Definition and 910 Threads

I have an electromagnetic field with a Poynting vector that has the following form in spherical coordinates: $$\bar{P}(R,\phi,\theta)=\frac{f(\phi,\theta)}{R^2}\bar{e}_{r}$$ The exact nature of f(\phi,\theta) is not known. Suppose I measure the flux of this vector field by a flat area...

Hi, physics undergraduate here. I don't know much about differential geometry yet, but I'm curious about this idea: Say I encounter a boundary value problem, and I'm not sure what coordinate system would be 'easiest' to solve the problem in. Is there some way to put the differential...

Coordinate System--Spring Vertical Hi! This is a question on the use of a coordinate system. In the princeton review, I don't understand the coordinate system they are using it; it doesn't make sense. That is, for a vertical spring, the net force on the mass is kx-mg. But, shouldn't it be...

Hi all. I am very puzzled by the following. Let x_1 and x_2 be two coordinate systems related by x_1=1-x_2. Now if y(x_1) = x_1 and z(x_2) = 1-x_2, then clearly y(x_1)=z(x_2). Now integrating the function in each coordinate system gives Y(x_1) = \int y(x_1) dx_1 = \int x_1 dx_1 =...

Hi! I am currently working with a linear PDE on the form \frac{\partial f}{\partial t} + A(v^2 - v_r^2)\frac{\partial f}{\partial \phi} + B\cos(\phi)\frac{\partial f}{\partial v} = 0. A and B are constants. I wish to find a clever coordinate substitution that simplifies, or maybe even...

Consider a simple two particle system with two point masses of mass m at x1 and x2 with a potential energy relative to each other which depends on the difference in their coordinates V = V(x1-x2) The lagrangian is: L = ½m(x1')2 + ½m(x2')2 + V(x1-x2) Obviously their total momentum is conserved...

Homework Statement A infinite long hollow cylinder has a narrow lengthwise cut and the potential on the cylinder is given by v(r,θ) = vo(θ/(2*pi)) Homework Equations V(s,theta) = Ao + Ʃ (n AnSnSin nθ + BnSn Cos nθ) The Attempt at a Solution boundary condition V(r,0)= 0 gives...

I am confused about one of the basic findings of relativity, that all coordinate systems are equal and there is no preferred coordinate system. A simple thought experiment is to consider three spacecraft called left, middle, and right. Left speeds off at half the speed of light in the left...

In McCauley's book Classical Mchanics: Transformations, Flows, Integrable and Chaotic Dynamics we are analyzing a coordinate transformation in order to arrive at symmetry laws. A coordinate transformation is given by q_i(\alpha) = F_i(q_1,...,q_f, \alpha). Then, to the first order Mccauley...

Hi I would like to know is there any way except using graph to find area element in cylindrical ( or Spherical) coordinate system? Thanks.

Just starting up school again and having trouble remembering some mathematics. Here's the problem. Find the inner product of ⃗a = (1, 45◦) and ⃗b = (2, 90◦), where these vectors are in polar coordinates (r, θ). Thanks =) 1st post here btw.

Homework Statement In the figure, let S be an inertial frame and let S' be another frame that is boosted with speed v along its x'-axis w.r.t. S, as shown. The frames are pictured at time t = t0 = 0: A) Find the Non-relativistic transformation (Galilean Transformation) between the two...

I would like to find a 3D coordinate of a point (X) on a circle, knowing two points on the circle (P1,P2) which represent the circle diameter and another point (P3) NOT on the circle but on its plane. Also known the length of the line from P2 to X, for example d. Another thing that may help, the...

Homework Statement For elliptical cylindrical coordinates: x = a * cosh (u) * cos (v) y = a * sinh (u) * sin (v) z = z Derive the relations analogous to those of Equations (168b-e) for circular cylindrical coordinates. In particular, verify that h_u = h_v = a * sqrt(cosh^2 (u) -...

Can someone help me with the conversion of this equation to Cartesian coordinates: 2cosθr + sinθθ (Due to formatting limitations, I just made the r_hat and theta_hat components bold-faced) I know the answer ought to be -(3y2)/[(x2+y2)+1] but I've tried every variation of the 3 main coordinate...

let x a point on complex manifold X, z_j a coordinate system at x , E a holomorphic bundle and let h_α be a holomorphic frame of E. After replacing h_α by suitable linear combinations with constant coefficients we may assume that h_ α is an orthonormal basis of E_{x}. Then an inner product <h_α...

Okay I need to rotate a parabola on a cartesian coordinate system, y=x^2 by 90 degrees about the origin (either direction) without using piecewise, or inverse functions. Basically I am trying to use translations and deformations to accomplish this. Anyone thoughts?

Homework Statement Please see the rotation formula in the attachment. Homework Equations The Attempt at a Solution I understand this formula rotates x,y into x',y' by some angle theta. Problem is, how is this formula derived? I cannot for the life of me visualize the cosine and...

Edit: Nevermind, it has been resolved. Homework Statement I have been attempting to solve what seems like a relatively pedestrian statics questions, but for some reason my answer is being marked as incorrect. The problem is as follows: Determine the magnitude and coordinate direction...

How do you define a right handed coordinate system for a basis which is not orthonormal?

find the equation of a circle whose center falls ont he line y=6-2x and which passes through the points A(-2,0) and B(4,0). poor in circles. how to even start?

Find the equation of the circle whose centre is (-3,4) and which touches the y-axis. how do i even begin?

Homework Statement http://img811.imageshack.us/img811/9092/captureykj.png The Attempt at a Solution The answer is also in the image above. I have no clue how to start this question. Could anyone be so kind to give me a hint on how I should approach this question? Thanks!

Homework Statement http://img15.imageshack.us/img15/1671/capturetwy.png The Attempt at a Solution Could someone please explain what is meant by "if v is constrained to 0"? Also how do you find a relationship between two axis of different coordinate systems? I really have no clue where...

The question I have is a bit strange. I do not have ANY formulas or equations given. I was only given bunch of points with r, theta, and z. Z being the depth. R being radius and Theta being the angle. I was wondering if there is a way to find a rough estimate volume of the following. R...

Homework Statement https://dl.dropbox.com/u/64325990/velocity%20of%20ball.PNG The Attempt at a Solution I was thinking I could just convert from metres to feet but turns out that's not the right answer. Am I suppose to change the coordinate systems so I get a distance vs time graph? I...

We may solve a function or check a theorem but sometimes the mathematics is easier when we switch from different coordinate systems. What can we look for that tells us changing is a good idea?

Homework Statement Consider a very thin conducting ring of radius R which contains a total positive charge of +Q coulombs. (a) Derive a formula for the z coordinate which gives the maximum value for the magnitude of E ring (Z)? (b) Suppose that the charged ring is oriented horizontally, as...

How would you graph a square of any dimension on the cartesian coordinate system?

Dear all, I'm wondering, how one could justify mathematically the equality \int O(E(\vec{x}_1,...\vec{x}_N)) exp(-\beta E(\vec{x}_1,...,\vec{x}_N)) d\vec{x}_1...d\vec{x}_N = \int g(E) O(E) exp(-\beta E) dE where O(E(x)) is an observable and g(E) the density of states. Is there a...

Given two points in 3D, is there a way to find the slope of that line.

note:The tensors in the new coordinates system are represented by X'. I have a question about the coordinate transformation of tensor. σmn=amianjσ'ij; (1) ωpq=apkaqlω'kl; (2) In the original coordinates system, we have σmn = Dmpnqωpq, (3)...

Homework Statement http://www.brookscole.com/math_d/special_features/stewart_shared/mathematica_labs/14-multipleintegrals/p05a.pdf Homework Equations The Attempt at a Solution My question concerns the (1) and (2) next to the figure of the rotating coordinate system...

Homework Statement Find the volume enclosed by the spherical coordinate surface ρ = 2sin∅ Homework Equations dV = ∫∫∫(ρ^2)sin∅dρd∅dθ The Attempt at a Solution (Sorry about my notation!) Alright, here's what I've done so far... Since the region is a torus, centered...

I have been studying gradience; divergence and curl. I think i understand them in cartesian coordinate system; But i don't understand how do they get such complex stuffs out of nowhere in calculating divergence in spherical and cylindrical coordinate system. Any helps; links or suggestion...

I know the orientations of the x-, y- and z- axes for a right-handed and a left-handed system. But that's for the cartesian coordinate system. How are the orientations of the coordinate axes for other coordinate systems defined? Also, i X j = k, j X k = i and k X i = j. How does this apply...

I have read over and over in various places about coordinate transformations, and understand the theory (really!), but can't find any worked examples of actual use of the transformation equations. Does anyone know of any web references or tutorials on the subject? To make things a little more...

In a uniformly rotating coordinate system the trajectories of freely moving objects are influenced by an apparent centrifugal and Coriolis force. Is there a coordinate system or metric (or both) in which these trajectories are geodesics instead?

The position operator in coordinate representation is: Xab=aδ(a-b) this is diagonal as expected The momentum operator turns out to look like Pab=-ih∂aδ(a-b) Now, this is not supposed to be diagonal because it does not commute with X. However it looks pretty diagonal to me. What am I...

In general relativity, we have a gravitational time dilation of: \frac{d\tau}{dt} = \frac{1}{\sqrt{1 - \frac{2GM}{rc^2}}} The term - \frac{2GM}{rc^2} appears to be based on the fact that gravity is attractive. If I understand correctly, if the curvature of space-time leads to attraction, then...

Homework Statement Given a symmetric tensor T_{\mu\nu} on the flat Euclidean plane (g_{\mu\nu}=\delta_{\mu\nu}), we want to change to complex coordinates z=x+iy, \,\overline{z}=x-iy. Show, that the components of the tensor in this basis are given by...

If we have any two orthonormal vectors A and B in R^2 and we wish to describe the circle they create under rigid rotation (i.e. they rotate at a fixed point and their length is preserved), how can we describe any point along this (unit) circle using a linear combination of A and B? I was...

Homework Statement Two particles are fixed to an x axis, particle 1 of charge q1 = 2.1x10^-7 C at x = 20cm and particle 2 of charge q2 = -4.00q1 at x = 70cm. At what coordinates on the axis is the net electric field produced equal to 0? Homework Equations The Attempt at a Solution...

I have looked at the definition of the metric tensor, and my sources state that to calculate it, one must first calculate the components of the position vector and compute it's Jacobian. The metric tensor is then the transpose of the Jacobian multiplied by the Jacobian. My problem with this...

Dear all, I am a medical doctor stuck with a mathematics problem. I have taken a project to map the 3D movement of a particular bone and describe its motion. My maths knowledge is a bit lacking. However using logic I felt that I would need to track 3 constant markers on the particular bone...

How can Eddington-Finkelstein coordinate be transformed into Lemaitre coordinate? I know the transformation between the Lemaitre and Schwarzschild coordinate, and also between Eddington-Finkelstein and Schwarzschild coordinate. So I tried to find the connection between Lemaitre and E-F...

I am trying to make a game in Chipmunk Basic using the arrow keys but I can't because I cannot figure out how. I have programmed in other Basic Softwares but I cannot figure out how to use the arrow keys and spacebar in my programs. An example (much simplified) of a game I am making is snake (if...

Spacetime curvature observer and/or coordinate dependent? In another topic several people suggested that spacetime curvature is not absolute, it apparently depends on the observer and/or coordinate system. Apparently if someone goes fast (whatever that might mean in relativity) curvature is...

Hi there, I am confused about the relationship between coordinate systems and reference frame in GR. I understand the coordinate systems can be used to describe reference frames, for example, Local inertial frames in GR can be defined by Riemann Normal Coordinates. However, take the...

So I've done some problems where a sphere intersects with a cylinder and I needed to find the volume of the intersected region using triple integrals. For example, if I needed to find the domain of integration for the intersection of the sphere $$x^2+y^2+z^2=a^2$$ and the cylinder...