Coordinate Definition and 910 Threads

In Nakahara's book, "Geometry, Topology and Physics" he states that it is, by construction, clear from the definition of a vector as a differential operator [itex] X[\itex] acting on some function [itex]f:M\rightarrow\mathbb{R}[\itex] at a point [itex]p\in M[\itex] (where [itex]M[\itex] is an...

Question: Triangle ABC is a right isosceles triangle with hypotenuse AB. M is the midpoint of Line AB. Write a coordinate proof to prove that Line CM is perpendicular to Line AB.

How do you transform a curvy coordinate system to that in euclidean space? An example will be greatly appreciated.

V′μ=((∂yμ)/(∂xν))*Vν This is a contravariant vector transformation. (Guys I am really sorry for making the formula above looks so incomprehensible as I still new to this.) For the y in the partial derivative, is y a function in terms of x? In that sense, is it formula that maps x to y? Is it...

Hi guys, I have a GR question. It is usually said that black holes have event horizons in which time freezes/stops relative to an outside observer. This happens in the Schwarzschild coordinate system. But are there any coordinate systems in which the coordinate time of the black hole and its...

I am using an algorithm that transforms from my sensor frame to North West Up and I want to instead use North East Down. I have attached the current algorithm. I also want to skip the first step in my algorithm. Here is the current algorithm: http://www.filedropper.com/transformationalgorithm...

r\rightarrow r-2qz and \psi\rightarrow\psi+q\cdot(r-qz), I don't know how to derive it, anybody know? This question results from the book "Optical Solitons: From Fibers to Photonic Crystals [1 ed.]" section 6.5

Hi, this may be a very basic concept, but I'm trying to develop coordinate systems for other planets from their right ascension and declination and prime meridians so that, given a location on that planet, you could visualize the sky and its stars.. I've been reading...

I am having a personal discussion with somebody elsewhere (not on Physics Forums) and we are stuck at the moment because of a disagreement that I narrowed down to the question whether, in the context of SR, two observers in different reference frames can choose the origin of their coordinate...

I was recently checking out a paper about gravitational energy and found a unexpected minor inconsistency when I did the calculation entirely in isotropic coordinates. I later tracked down what caused it, and it surprised me a bit, so I'm wondering if others were aware of this. Basically, I'd...

I've come up with a curious two-part question while working on a map program: What is the minimum number of points necessary in order to transform an NxN adjacency matrix into a coordinate matrix in terms of N given Euclidean space? As this question relates to map-making, where I don't...

Consider a flat Robertson-Walker metric. When we say that there is a singularity at $$t=0$$ Clearly it is a coordinate dependent statement. So it is a "candidate" singularity. In principle there is "another coordinate system" in which the corresponding metric has no singularity as we...

If you look at Newtonian gravity, there is no major deal with coordinate systems. I am guessing we use coordinate systems because in general relativity we think of coordinate systems as different frames of references and that all frame of references must have the same laws of physics. Is that why?

Although the speed of light is constant in GR, within coordinate spacetime the speed of light varies. For example, light travels more slowly near a black hole than in remote space. The same is theoretically true of the speed of gravity. But is there any supporting empirical evidence?

Hi guys So I am having trouble reparameterizing the geodesic equation in terms of coordinate time. Normally you have: \frac{d^2 x^{\alpha}}{d \tau^2} + \Gamma_{nm}^{\alpha} \frac{d x^{n}}{d \tau}\frac{d x^{m}}{d \tau} = 0 Where \tau is the proper time. I class we were told to express the...

Homework Statement A tensor and vector have components Tαβγ, and vα respectively in a coordinate system xμ. There is another coordinate system x'μ. Show that Tαβγvβ = Tαβγvβ Homework Equations umm not sure... ∇αvβ = ∂vβ/∂xα - Γγαβvγ The Attempt at a Solution Tαβγvβ =...

Hey there, I trying to understand the following coordinate transformation of the equation of continuity (spherical coordinates) for a vaporizing liquid droplet\frac{\partial \rho}{\partial t} + \frac{1}{r^2} \frac{\partial}{\partial r} (r^2 \rho v) = 0 into \epsilon \sigma \frac{\partial...

how do i write vectors in polar coordinate? And what will the azimuth coordinate represent? I was trying to figure out the vector connecting a ring to its center using polar coordinates, so that i would perform an integration over d(phi) (finding the electric field due to a semicircle at the...

How do I find the polar coordinates of the points on the polar curve r=cos(theta)+sin(theta), 0(greater than or equal to)(theta)(less than or equal to)(pi), where the tangent line is horizontal or vertical? I know that I need to convert the coordinates to x & y and then take the derivative of...

Hello I have some questions to understand much more better the Gauss's law in Cartesian coordinate. 1-when can we use Gauss's law and it's integral to solve a question easier in Cartesian coordinate? 2-Is it difference to use a cylindrical or cube shape for a plane that disturbed some...

I'm asked to figure out how the so-called "coordinate space matrix elements" relate to "momentum space matrix elements <p|H|p'> but I don't understand what they are. any idea on how <x|H|x'> is defined? thanks in advance.

Homework Statement Suppose two observers O and O', whose positions coincide , each sets up a set of 2D cartesian coordinates (x,y) and (x',y') respectively to describe the position of a certain object at a fixed point . Derive a set of formulae for one observer to convert the other observer's...

Hello All I have got a very basic Math query here and hope people will not get turned off with the nature of this simple query. My query goes like this: variable X makes jump by factor +4. at the same time, Y makes a jump by factor +2 in coordinate terms, I would have a series like : (4,2)...

EDIT: There was an issue where half of the post was missing, so I apologise but i have redone it I was not sure if this was the most appropriate forum for this or not, so feel free to move if needed. 1. Homework Statement A football (soccer ball) with a diametre of 0.44m is tracked using a...

Homework Statement An alpha particle (the nucleus of a helium atom) is at rest at the origin of a Cartesian coordinate system. A proton is moving with a velocity of v towards the alpha particle in the xˆ direction. If the proton is initially far enough away to have no potential energy, how...

Hello all. I didn't know whether this fit pre-university math so I posted here. This is exercise's 1.15 from Kleppner & Kolenkow. By relative velocity we mean velocity with respect to a specified coordinate system. (The term velocity, alone, is understood to be relative to the observer's...

Hi. I have been looking at the coordinate charts for the unit circle x^2 + y^2 = 1. In the notes I have the circle is split into 4 coordinate charts the first being - ##U_1## : x>0 , ##A_1## = y (PS without the symbols tab I have used A for the letter phi ) There are 3...

Homework Statement As shown in the image below, can I use 2 different co-ordinate systems when drawing the free body diagram for each object? Homework Equations The Attempt at a Solution

Q: How does one do a coordinate transformation in momentum space while insuring conservation of momentum? I have a several particles with momentum components P_x , P_y , P_z . I would like to rotate the x, y, and z axis. By angle θ in the x/y and angle Θ in the y/z . So giving new...

Homework Statement Convert to the two other coordinate systems: θ = π/4Homework Equations tan = x/y r = √(x^{}2 + (y^{}2)The Attempt at a Solution The tangent equals one, so doesn't this make just the line x = y? But the cylinder (I'm assuming since the second part is the same exact problem but...

I've been trying to come up with a oordinate free formula of Christoffel symbols. For the Christoffel symbols of the first kind it's really easy. Since \Gamma_{\lambda\mu\nu} = \frac{1}{2}\left( g_{\mu\lambda,\nu}+g_{\nu\lambda,\mu} - g_{\mu\nu,\lambda}\right) we can easily generalize the...

The answer is E. Since the line is passing the parable at x = 1 and 2 I used between these values to satisfy the inequality(x − 1)4< (x − 1)X = 1,5 (1,5 -1)4 < (1,5 -1) 0,0625 < 0,5 Is this correct?

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 Prove: \cos\alpha\cdot\cos\alpha'+\cos\beta\cdot\cos\beta'+\cos\gamma\cdot\cos \gamma'=\cos\theta See drawing Snap1 Homework Equations None The Attempt at a Solution See drawing Snap2. i make the length of the lines 1 and 2 to equal one, for simplicity. The...

During the course of working with inertial measurement units (IMU) I have run into a problem. The issue is that an IMU reports accelerations relative to the IMU's orientation rather than it's initial orientation. The IMU's initial orientation is the identity quaternion (1,0,0,0). All changes...

The problem I am having is a problem in my textbook. It says that if we have xy Cartesian coordinate system, and if we then have a rotated coordinate system x'y', then to get the vector in the x'y' in terms of the xy system, we use the following arguments for the unit vectors: i' = icos\Phi +...

Hi everyone, I have to find out how to do cross and dot product for two vectors in non-orthogonal coordinate system. thanks

Hi everyone, I am doing MD simulation for zirconium (hcp). I have to input some orientation for crystal in simulation. But i have orientation in 4-index bravais miller indices. and i have to convert (plane and direction) it from 4-index to 3-index orthogonal coordinate system. Please help me...

If two orthogonal coordinate systems (xyz and x'y'z') share a common origin, and the angles between x and x', y and y', and z and z' are known. What is angle between the projection of z' on the xy plane and the x axis? Thank you for your help!

Let A(1, 2), B (3,4), C( x, y) be points such that (x- 1) (x-3) +(y-2) (y-4)=0. Area of triangle ABC=1. maximum number of positions of C in the xy plane is (a) 2 (b) 4 (c) 8 (d) None of these I have tried using the staircase formula which gives me something like x-y=2. Therefore I see only...

I am sure this is not the best description of the problem, so let me know how I can clarify. Say there are 2 coordinate systems, with one orbiting around the other. Call one fixed ƒ and the other rotating ρ. The goal is to find the transform between the two frames. What's known is 1) A...

Do unobserved particles exchange information with other particles? If not then they are not only unobserved but also un-observing, which would seem to mean that they not only do not have a well defined position but that the very concept of position does not exist for them, nor does distance or...

How can I geometrically interpret this coordinate transformation (from x,y space to \check{x},\check{y} space)? x = \check{x}cos(β) - \check{y}sin(β) y = \frac{1}{2}(\check{x}2 -\check{y}2)sin(2β) -\check{x}\check{y}cos (2β)

I apologize for posting this question on a physics forum because it has a science fiction origin. However, I thought that real astronomers may have a real science answer to the question, so here goes. Imagine two parties from distant parts of the galaxy in communication with each other...

Homework Statement A ball of mass m travels with speed v, hits a stationary ball with the same mass m and after collision they both move at speed v/2. From the point of view of the first ball the total momentum is -mv and after the collision it is 0. why isn't the law of conservation of...

Hi, I was wandering, sometimes in physics, to get acceleration from a velocity time graph, you would have to find the gradient of the tangent of the curve. But in other graphs like say Voltage current graph, if you want to find the resistance at any point (Which is V/I) you simply take the...

I'm not sure if it is the right place to post my questions to. please let me know if this should be somewhere else. 1. let each of the vectors $A=5a_x-a_y+3a_z$ $B=-2a_x+2_ay+4a_z$ $C=3a_y-4a_z$ extend outward from the origin of the cartesian coordinate system to points A,B, And...

Can someone please help me with this? I can't for the life of me figure out how to do these points. How do I line up the x, y, and z? I just can't grasp it and can't find anything online.

how can we write and interpret Lorentz generators in light cone coordinates?

Hello, i don't know if my question is well posed, if i have a symmetric tensor Sij = (∂ixj + ∂jxi) / 2 with xi cartesian coordinates, how can i transform it in a spherical coordinates system (ρ,θ,\varphi)? (I need it for the calculus of shear stress tensor in spherical coordinate in fluid...