Coordinate Definition and 868 Threads

[b]1. Homework Statement [/ In 3-D coordinate space, any two of the coordinate angles must … Select one: a. sum to less than 1 b. be greater than 90° but less than 180° c. each be greater than 45° d. sum to greater than 90° (if they are both less than 90°). e. have cosines less than...

Homework Statement If u know the value of two coordinate angles there is an ulimeted amount of possibility for finding the third coordinate angle A. True B. False Homework Equations The Attempt at a Solution I .not too sure about this one any suggestions would be appreciated I...

Homework Statement If z is up and x is west they y is what direction A. West B. Down C. Up D. East E. South Homework Equations The Attempt at a Solution I tried applying the rule and obtained south as my answer would anyone be able.to provide a.solution

Let's say we have a mass with an object orbitting with constant speed in a circular orbit and a distant observer Bob. According to Bob's coordinate system, the orbit is circular at a speed v and a constant inward coordinate acceleration a. The coordinate acceleration is just what is inferred...

Homework Statement So I am not sure how to multiply these two (A*R^2) together. Homework Equations A=( x^2 + y^2 + z^2 ) (xe + y e + z e ) Where x represents the three vector compones I also have R^2=x^2+y^2+z^2 The Attempt at a Solution Is the product of A (x^3e + y^3 e + z^3...

Hellow everybody! A simples question: is it correct the graphic representation for covariant (x₀, y₀) and contravariant (x⁰, y⁰) coordinates of black vector?

http://i.imgur.com/MDigPh5.png if i have my original coordinate (white) and i am transforming this into the red coord. , could someone explain to me why y=y'cos\phi is incorrect and why y'=ycos\phi is correct?

Recently I've been studying about orthogonal coordinate systems and vector operations in different coordinate systems.In my studies,I realized there are some inconsistencies between different sources which I can't resolve. For example in Arfken,it is said that the determinant definition of the...

Homework Statement A hydrogen chloride molecule (HCl) has a partial positive charge on the hydrogen atom and a partial negative charge on the chlorine atom. The HCl molecule is placed at A. There will be force on the bromide ion in the +x direction. B. There will be force on...

Homework Statement Hi, I am not sure if this is the right place for my question but here goes! The stress tensor in the Si coordinate system is given below: σ’ij = {{-500, 0, 30}, {0, -400, 0}, {30, 0, 200}} MPa Calculate the stress tensor in the L coordinate system if: cos-1a33=45°, and...

In a coordinate system two axes are inclined at an acute angle θ. Is this coordinate system different from a coordinate system in which the axes are inclined at an angle (180 - θ)? if we look at the four quardents in either of the above set of axes, both are included giving the impression that...

Given a basis \mathfrak{B}=\lbrace\mathbf{e}_{i}\rbrace it is possible to represent a vector \mathbf{v} as a column vector \left[\mathbf{v}\right]_{\mathfrak{B}}= \left(\begin{matrix}v^{1} \\ v^{2} \\ \vdots \\ v^{n}\end{matrix}\right) where the v_{i} are the components of \mathbf{v} relative...

I'm so confused about finding an angle, theta in this illustration. With having three coordinate information, how can I calculate the theta using dot product? I would easily find the angle by using trigonometric formula if I ignore the z-axis. But I want to solve this problem with...

Homework Statement So for this problem we are shown a right triangle with point B at (2,1), C at (7,0) and A(x,y). 'A' also happens to rest at the right angle of our triangle. What is the coordinate of 'A' The Attempt at a Solution I tried this one a couple ways. For example the dot...

Homework Statement We have two coordinate functions of time, as follows: x(t) = 5 + 2t ; y(t) = -3+3t+2t2. Find velocity \vec{v}, acceleration \vec{a}, tangential acceleration \vec{a_t}, normal acceleration \vec{a_n} functions of time and their magnitude's functions of time. Homework...

Coordinate question -- "above x-z plane" Homework Statement Say I want to verify a condition is true that ∇∇F = 0 above the x-z plane.Where F(x,y,z). Does the "above x-z plane" mean in the x-z plane i.e. we evaluate ∇∇F(x,0,z) ?

Homework Statement Hey guys. So here's the problem: Consider an ordinary 2D flat spacetime in Cartesian coordinates with the line element ds^{2}=-dt^{2}+dx^{2} Now consider a non-inertial coordinate system (t',x'), given by t'=t, x'=x-vt-\frac{1}{2}at^{2} (1) What is the metric...

Homework Statement (a) Consider a system with one degree of freedom and Hamiltonian H = H (q,p) and a new pair of coordinates Q and P defined so that q = \sqrt{2P} \sin Q and p = \sqrt{2P} \cos Q. Prove that if \frac{\partial H}{\partial q} = - \dot{p} and \frac{\partial H}{\partial p} =...

Homework Statement Integrate the double Integral: 6xdydx in polar coordinates The y goes from bottom limit of x(3)^(1/2) to the top limit of (1-x^2)^(1/2) the x goes from 0 to 1/2 Homework Equations The Attempt at a Solution So I graphed it, and it looks like a semi circle on...

In SR there is a whole family of so called inertial observers that are defined as those observers that move at relative constant speed with respect to one another, whose descriptions of nature are all equivalent and whose spacetime coordinate are related by Lorentz transformations i.e. those...

Hi all, The context of this problem is as follows: I'm trying to implement a discontinuous finite element method and the formulation calls for the computation of line integrals over the edges of the mesh. Anyway, more generally, I need to evaluate \int_{e}f(x,y)ds, where e is a line segment...

Write a short FORTRAN90 subroutine to convert Cartesian coordinates (x, y, z) to spherical polar coordinates (r, q, f) using • Write a FORTRAN90 program which uses this subroutine to convert the following (x, y, z) coordinates which are read from a text file and stored within a single vector...

Homework Statement I don't know why I'm having trouble here, but I want to show that, if we let t = t(\theta) and q(t(\theta)) = q(\theta) so that both are now dependent coordinates on the parameter \theta , then L_{\theta}(q,q',t,t',\theta) = t'L(q,q'/t',t) where t' =...

I have been reading an introductory book to General Relativity by H Hobson. I have been following it step by step and now I am stuck. It is stated in the book that: "It is straightforward to show that the coordinate and dual basis vectors themselves are related... "ea = gabeb ..." I have...

## \vec{r}=\rho \cos \varphi \vec{i}+\rho \sin \varphi \vec{j}+z\vec{k} ## we get \vec{e}_{\rho}=\frac{\frac{\partial \vec{r}}{\partial \rho}}{|\frac{\partial \vec{r}}{\partial \rho}|} \vec{e}_{\varphi}=\frac{\frac{\partial \vec{r}}{\partial \varphi}}{|\frac{\partial \vec{r}}{\partial...

Homework Statement The Attempt at a Solution I already know how to do a), but what I am wondering is what the question means by expressing position in the terms of those unit vectors.

Hello PF members! I have a problem regarding coordinate and non-coordinate bases. As I understood from my course in GR, the partial derivatives of a coordiante system always commute: [\frac{\partial}{\partial x^i}, \frac{\partial}{\partial x^j}] = 0 . Which is not necessarly true for...

Homework Statement (a) Starting from a point on the equator of a sphere of radius R, a particle travels through an angle α eastward and then through an angle β along a great circle toward the north pole. If the initial position is taken to correspond to x = R, y = 0, z = 0, show that its...

Hi I didn't post this in homework help, as I didn't feel my question belonged there. If it doesn't belong here, my apologies. I recently took an exam and it turns out I got the first question wrong according to my professor. The problem states: "In the diagram four vectors are represented by...

How to determine the X coordinate of the red point if i know the Y coordinate and the angle between the adjacent side and the hypotenuse in the formed right triangle(see the image)? I don't know the length of the hypotenuse and the adjacent side of the triangle, i know only the angle between the...

I have a question that i been trying to solve which seam simple but been having trouble. Today I thought about rotation matrix and how the following problem would be solved. Initial Coordinate system (x,y,z) a rotation is desired about x let's say α=30 degrees so that a new coordinate...

Hi guys, I would like to know if the answer given to this thread is correct https://www.physicsforums.com/showthread.php?t=457405 I got the same doubt, is the expression for the tensor given in cartesian coordinates or is it general to any orthogonal coordinate system? Thanks in advance

Insect uses mechanical "gears" to coordinate jumping journalist report: http://www.csmonitor.com/Science/2013/0912/Insect-uses-gears-to-jump-study-finds scientific report: http://www.sciencemag.org/content/341/6151/1254

Hello, Please forgive me if it's in the wrong sub-forum because don't know where to place it. I need help solving this problem it's chapter 1 and in our class we are already in chapter 5 so I might sound like a fool asking the teacher about it, I was revising and decided to do some questions...

I have a (probably trivial) question about coordinate charts. I've been studying Sean Carroll's lecture notes on General Relativity. I'm on my second re-read and I'm trying to make sure I understand the basics properly. I hope the terminology is correct - this is my first use. Carroll cites...

Hello, I would like to rotate the Cartesian coordinate system ( i=(1,0,0); j=(0,1,0); k=(0,0,1) ) so that angles between new and the old axes be equal to α, β and γ, respectively. Is any simple way similar to the Euler transformations to accomplish that?

Hi all, Note: The text below is the motivation for my question. To jump to the question immediately, please skip to the line that says HI! I have a set of data points, let's call it A, and I ran principal component analysis to get the top 3 principal components to be able to represent the...

a =(x,y), b =(h,k) a cross b =? I have idea what to type on google. Is that doing like matrices , a cross b = xk-hy? thanks.

Two point charges of Q1 = +37 nC and Q2 = +70 nC are located at points (1,3,0) m and (0,0,2) m, respectively. Q : Calculate the force exerted on Q2 by Q1. Attempt : I applied phythagoras theorem to find the distance between Q1 and Q2, I then applied coulombs force law equation directly...

Homework Statement At t=0, a particle leaves the origin with the velocity of 9.0m/s in the positive y direction and moves in the xy plane with a constant acceleration of ( 2.0i-4.0j) m/s ^2 . At the instant the x coordinate of the particle is 15 m , what is the speed of the particle ...

I am somewhat puzzled after reading that polynomials can be vectors, this concept confuses me. For instance, they can say that a basis for polynomials P_2 can be. B=\{1+t^{2},t+t^{2},1+2t+t^{2}\} In this case will the mapping [1+t^{2}]_{B} be [1,0,0] or [1,0,1]?

The correct one is 2nd, but why not first? Please guide , or tell me any link that relate to this derivation. Thanks

Homework Statement In Cartesian coordinaate system, we describe the rotation of a cylinder. The axis of the cylinder has the same direction as the basis vector e3. Angular velocity is described by vector w = 2e1 - 5e2 + 7e3 rad/s. I must find the velocity vector (v) of a point P that is...

Homework Statement Hi I have a coordinate system (x', y') and a vector v'=(1, 0) here. There is a different coordinate system (x, y), which is rotated about the y-axis relative to (x', y') by an angle Ω. I am trying to express v' in the system (x, y). At first what I tried to do was to...

http://www.answers.com/topic/radial-and-transverse-components From the above link, 1) e θ is a unit vector perpendicular to r in the direction of increasing θ. Where is the direction of increasing θ? Is that a circle? θ Increase from 0 to 2∏.then eθ moves in a circle? direction always...

Hello, Just as a warning before anyone reads my question I am not a mathematician, just an engineer with moderate math skills he wants to expand. So I'm writing some engineering software which involves defining/interation/modification of geometry within a cartesian system but I currently...

I want to solve a following problem. Imagine a collection of massive points. Each point has mass, position, velocity, moment of inertia, orientation and spin. We can calculate its total center of mass, total momentum and total angular momentum. The task is to transform the coordinate system...

Homework Statement Hello Guys, I am reading Hobson's General Relativity and I have come across an exercise problem, part of which frustrates me: 3.20 (P. 91) In the 2-space with line element ds^2=\frac{dr^{2}+r^{2}d\theta^{2}}{r^{2}-a^{2}}-\frac{r^{2}dr^{2}}{{(r^{2}-a^{2})}^{2}} and...

The Schwarzschild spacetime can be foliated by 2-sphere, which are spacelike hypersurfaces of constant t and r (Schwarzschild coordinates) with a normal vector ##\partial_t## (outside the horizon). Because a 2-sphere has no center, the coordinate r is not the radius of the sphere and we consider...

Previously, before getting into relativity, I've always thought of a 'reference frame' of basically an "observer carrying a coordinate system" - where I thought of an observer as anything which could record information of positions and velocities of particles etc. Now, however, I'm reading a...