Coordinate system Definition and 191 Threads

Homework Statement Show that, owing to the rotation of the Earth on its axis, the apparent weight of an object of mass m at latitude λ is : m((g-ω^{2}Rcos^{2}λ)^{2}-(ω^{2}Rcosλsinλ)^{2})^{1/2} where ω is the angular velocity of the Earth and R its radius. The first space travellers to reach...

Homework Statement This is a 2 part question. I'm fine with the first part but the 2nd part I'm struggling with. The first part asks us to calculate the double integral, \int\intDx2dA for, D = {(x,y)|0≤ x ≤1, x≤ y ≤1} For this part I got an answer of 1/4. For the 2nd part we introduce a new...

Firstly; is there a difference between the "regular" polar coordinates that use \theta and r to describe a point (the one where the point (\sqrt{2}, \frac{\pi}{4}) equals (1, 1) in rectangular coordinates) and the ones that use the orthonormal basis vectors \hat{e}_r and...

Hello! I have a problem. How can I convert a left part from picture which is in coordinate system (r, s) to coordinate system (x, y) and then to coordinate system (ζ, η) (right part). I need Jacobian matrix because of integration some function above this region. Any helpful links or...

Hi PF, I have always wondered what was meant when my teachers told me that a vector is the same no matter what coordinate system it is represented in. What is it exactly that is the same? I mean the components change. So the only thing that I can see remains the same is the length of the vector...

Homework Statement Please read the attachment =) All the formulas I was given are also on a separate attachment I initially thought the answer was the last one because I did rf-ri and subtracted across and got 0 mi + 25mj but I am not sure =[ Homework Statement

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...

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

Can someone help me with the conversion of this equation to Cartesian coordinates: [SIZE="4"]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...

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...

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

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...

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

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

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...

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...

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?

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...

Homework Statement The point is (0, -8, 0) r≥0 0≤θ≤2∏ 0≤\varphi≤∏ Homework Equations The Attempt at a Solution So here is what I've done so far: I know that r=8 because x and z are 0 I know that θ=∏/4 or 3∏/4, but which one? both of these satisfy the following equation...

Hey guys, I am having some problems with the concept of inertial/non-inertial frames of reference and their applications in engineering dynamics. So I've learned that a given frame of reference is defined to be non-inertial when something in the studied system can only be explained through...

Homework Statement (a) In cylindrical coordinates , show that \hat{r} points along the x-axis is \phi = 0 . (b) In what direction is \hat{\phi} if \phi = 90° Homework Equations The Attempt at a Solution here is my solution. for a. \vec{r} = \rho cos \phi \hat{i} + \rho...

Hi, I have to solve a numerical problem namely how air is flowing first through a porous medium followed by streaming of the air coming out of the porous medium in a very narrow channel flowing to the ambient (journal porous air bearing). This problem can be described with the use of two...

Homework Statement i have the divergence in the (x,y,z) Cartesian as \frac{dA_x}{dx}+\frac{dA_y}{dy}+\frac{dA_z}{dz} and the assignment is to transfer it to cylindrical system (r,{\phi},z), by any way i choose. Homework Equations tried with the chain rule, but i am doing...

we know that for any (x, y) in Cartesian system, there is such (r, θ) in Polar system, so x = r * cosθ and y = r * sinθ how you can calculate what corresponds to (Δx, Δy) in polar system? how come Δx * Δy = r * Δr * Δθ? Maybe this is very stupid question and has obvious answer...

In a right-handed cartesian coordinate system the divergence and curl operators are respectively: \nabla \cdot A= \frac{\partial A_{x}}{\partial x}+\frac{\partial A_{y}}{\partial y}+\frac{\partial A_{z}}{\partial z} \nabla \times \mathbf{A}= \begin{vmatrix} \widehat{x} & \widehat{y} &...

Homework Statement I was trying to figure out how to derive acceleration in spherical coordinates, and I realized that I need to find the projection of each spherical unit vector [ e(r), e(θ), and e(φ)] onto each Cartesian unit vector [î, j, and k], but I'm not quite sure as to how to do that...

In school I've always learned that tensor transformations took the form of: \mathbf{Q'}=\mathbf{M} \times \mathbf{Q} \times \mathbf{M}^T However, in all the recent papers I've been reading. They've been doing the transformation as: \mathbf{Q'}= \frac {\mathbf{M} \times \mathbf{Q}...

Do we need a metric field on a manifold so as to specify a coordinate system on it?

I've already post this, but I've done it in the wrong section! So here I go again.. I've a doubt on the way the infinitesimal volume element transfoms when performing a coordinate transformation from x^j to x^{j'} It should change according to dx^1dx^2...dx^n=\frac{\partial...

Does performing a rotation of the usual coordinate system ct,x in the minkowsky spacetime makes sense? I guess it doesn't, but more than this i think that there is something that forbids it, since i could make coincident the 'lenght' axis of the non rotated coordinate system (observer A) with...

Very simple question: Let x^0,x^1,...,x^n be some fixed coordinate system, so that the infinitesimal volume element is dV=dx^0dx^1...dx^n. Then any change to a new (primed) coordinate system x^{0'},x^{1'},...,x^{n'} transforms the volume to dV=\frac{\partial (x^0,x^1,...,x^n)}{\partial...

When in 2D, the coordinates of a place in space vary depending on the coordinate axes that are being used given by: A_{x}^{\prime}=A_{x}\cos\theta+A_{y}\sin\theta (1) and A_{y}^{\prime}=-A_{x}\sin\theta+A_{y}\cos\theta (2) Now I am trying to reverse it - to show what A_x and A_y are in...

Hi everyone I have a little problem in understanding the trasformation of vectors component when passing to a different coordinate system (abbreviated CS). Theory says that the components of a vector in the first CS x with component (V^0,V^1,...,V^n) will transform changing CS according to...

what does this mean please: bisectrix of the rectangular coordinate system

Hello, I have a question related to coordinate transform. If this is not the right section please feel free to move this thread. My problem is the following: I have a positioning system to move an antenna, that allows me to perform scans according to a great circle coordinate system. Check...

Homework Statement What are the signs of the forces (positive + or negative -) acting on both situations? Situation 1: Situation 2: Homework Equations Not really necessary The Attempt at a Solution I'm not sure about Situation 1 at all, but I think I got Situation 2: If I have this...

I feel I may have improperly posted this thread https://www.physicsforums.com/showthread.php?t=469331" but am just not as knowledgeable in my matrix math as I need to be. One (me) would think that somehow you should be able to get a rotation matrix from these two systems. Homework Statement So...

Hey everyone, I'm working on my degree and have started getting into some deeper lin alg than I took previously regarding coordinate system transformations. I was hoping someone might be able to shed some light on it for me. I'll do my best to explain the problem .. I have a global...

Dear Friends, I have below query Available data: Point1 (r1,theta1,phi1) Point2 (r2,theta2,phi2) where in spherical coordinate system r(i)=radius theta(i)=angle phi(i)=azimuth Required output: Line of intersection by individual planes generated by each point i.e. from point1 we...

Homework Statement A block of mass m slides down a plane inclined at an angle theta with initial velocity v down the slope and with friction coefficient mu. Find T, the time in which the block comes to a rest due to friction. Use coordinates with y vertical and x horizontal. Homework Equations...

I don't understand what's wrong with it:

Hello, I am trying to understand the Maxwell Stress Tensor. Specifically, I would like to know if it is coordinate-system dependent (and if so, what the expressions are for the stress tensor in cylindrical and spherical coordinates). Griffiths gives the definition of the maxwell stress tensor...

Lets say I have Coordinate Frame's A and B. and... I have the coordinates of the 3 principle axes of B in terms of Frame A, So for a simple example, a rotation of +pi/2 about the z axis of A would yield the following mapping of the xyz axes of B in terms of Frame A: XA -> -YB YA -> XB ZA ->...

Homework Statement Starting from one oasis, a camel walks 82.021 ft in a direction 30 degrees south of west and then walks 30 km toward the north to a second oasis. Without using a coordinate system, calculate the magnitude and the direction of the displacement from the first oasis to the...

A charged particle in a magnetic field is spiralling along a path defined in cylindrical coordinates by r = 1 m and θ = 2z rad (where z is in meters). The speed along the path is constant at 3.87 km/s. What is the z-component of the velocity, vz, in cylindrical coordinates? My attempt...

Hi! I see there are three 3D coordinate systems based on either 3 number (cartesian), 2 numbers and 1 angle (cylindrical) and 1 number and 2 angles (spherical). So can't there be a system based on 3 angles? Thank you.

Homework Statement I will to explain this without a diagram. Consider a coordinate system(1st quadrant) where the x and y-axis both stop at 7 units (i mean the boundary), there are two points P(3,3) and Q(4,4). How many points can R be positioned such that PQR is an isosceles triangle...

Currently I am using a graphying application called "Autograph" and modeling a building with a dome shaped roof on top. I need to define parabolic shapes in 3d system. But i can't do it ( my math knowledge is pretty elementary) What would be the basic parabolic function in 3d that i can base...

Hello to all, I am currently studying computer graphics and I have came up with the following problem. Consider that we have three coordinate systems, let's say CSA1, CSA2 and CSA3 that have the same origin and differ by a rotation. That is to CSA2 connects to CSA1 by R12 and CSA3 to CSA1 by...