Coordinate system Definition and 200 Threads

I am trying to learn GR. In two of the books on tensors, there is an example of evaluating the inertia tensor in a primed coordinate system (for example, a rotated one) from that in an unprimed coordinate system using the eqn. ##I’ = R I R^{-1}## where R is the transformation matrix and...

Why should a person prefer irrational coordinate system over rational? My friend stated that its because most lines such as ##y=e## cannot be plotted on a rational grid system. But that cannot be true since ##e## does have a rational number summation ##2+1/10+7/100...## which can be utilised to...

Homework Statement Coordinates of a particle which moves on a xy coordinate system given with: x=-(5m)sinωt y=(4m)-(5m)cosωt In these equlations t's unit given as second, and ω's unit second^-1. A-) Found velocity and acceleration components when t=0 B-) Write equlations for position and...

I have an issue with the definition of coordinate system in differential geometry vs the definition of coordinate system in linear algebra. The post is a bit long, but it's necessary so that I get my point across. Let ##V## be an ##n##-dimensional normed space over the reals and equip ##V##...

Is there a universal criteria to determine if a coordinate system is global? I think that it is sufficient for the determinant of the metric to be non-zero in order for a coordinate system to be global. Is this so? For example, take the metric ##ds^{2} = \ell^{2}(-\cosh^{2}\rho\ dt^{2} +...

Homework Statement Say I have some sort of a vector field in the cylindrical coordinate system \vec{F}(r, \Theta, z) = f(\vec{A}(r,\Theta,z),\vec{B}(r,\Theta,z)) How do I switch to the Cartesian coordinates? More precisely, how do I transform A_r = g(A_x,A_y,A_z), A_\Theta = h(A_x,A_y,A_z)...

I want to understand what changing coordinate system means for hands of clock. Let's say the clock only has hour and minute hand. It can move let's say just in the upper 180 deg. of the clock (as shown in the figure). The area between the two hands is V1, and the rest is V2. Depending on the...

I am learning about the polar coordinate system, and I have a few conceptual questions. I understand that in Cartesian coordinates there is exactly one set of coordinates for any given point. However, in polar coordinates there is an infinite number of coordinates for a given point. I see how...

Homework Statement On the surface of a river at ##t=0## there is a boat 1 (point ##F_0##) at a distance ##r_0## from the point ##O## (the coordinate beginning) which is on the right side of the coast (picture uploaded below). A line ##OF_0## makes an angle ##θ_0=10°## with the ##x-axis## whose...

Homework Statement Below: Jac = Jacobian matrix; ξ = d/dφ for some continuous parameter φ which labels different points on the worldline. (I'm sorry for my poor English.) Consider a new coordinate system xµ' which differs from the original Cartesian coordinate system xµ; the Cartesian...

Hello! I understand the the polar coordinate system without vectors. But when it is related to vector, it is confusing. Do the unit vectors r and phi keep changing? How do I interpret it as they changes? For example, F = 2 r + 3 phi. Based on the vector addition and scale multiplication, it...

Homework Statement Let $$\vec H = ih_4^{(1)}(kr)\vec X_{40}(\theta,\phi)\cos(\omega t)$$ where ##h## is Hankel function of the first kind and ##\vec X## the vector spherical harmonic. a) Find the electric field in the area without charges; b) Find both fields in a spherical coordinate system...

Homework Statement [/B] In a set of axes where the z axis is the axis of rotation of a finite rotation, the rotation matrix is given by ## \left[ \begin{array}{lcr} &\cos\phi \ \ \ &\sin\phi \ \ \ &0 \\ & -\sin\phi \ \ \ &\cos\phi \ \ \ &0 \\ &0 \ \ \ &0 \ \ \ &1 \end{array} \right]##...

(Note that the title of this thread might be incorrect - I'm just drawing on the vocabulary people use when discussing Lagrangian Mechanics...) Hi, I'm trying to set up a coordinate system to represent points in space where one of the coordinates is the distance along a parametric curve, one is...

Let's say we have r=R( theta, phi, t) on the surface of the particle and need to find the normal vector in Spherical Coordinate system. We know that, the unit vector =grad(r-R( theta, phi, t)) / |grad((r-R( theta, phi, t))| where grad is Spherical gradient operator in term of e_r, e_\theta...

MENTOR note: moved from General Math hence no template What would be the Y-Axis if: X-Axis: theta=266.4 phi=-28.94 Z-Axis: theta=192.85 phi=27.13 where: theta=atan(Y/X) phi=asin(Z/R) My thinking, theta is +90 from X-Axis and phi is -90 from the Z-Axis. Is the Y-Axis theta=356.4 phi=-62.87?

Studying the acceleration expressed in polar coordinates I came up with this doubt: is this frame to be considered inertial or non inertial? (\ddot r - r\dot{\varphi}^2)\hat{\mathbf r} + (2\dot r \dot\varphi+r\ddot{\varphi}) \hat{\boldsymbol{\varphi}} (1) I do not understand what is the...

Homework Statement I have an a-b coordinate system which is skewed with an angle = 60 deg. I also have a particle position defined by vector V1 (a1, b1, 0) which follows the coordinate system. The problem I have is that I need to get V2 (a2, b1, 0) which is perpendicular to V1. Homework...

Homework Statement imgur link: http://i.imgur.com/pb14Q4Q.png Homework EquationsThe Attempt at a Solution [/B] The thing I don't understand is where the first two terms of each 2nd order ODE came about. I understand that they are there because the coordinate system is rotating, but when...

It can be found in any advanced calculus textbook the proof that, for a "well-behaved" space curve, the acceleration vector can be decomposed into components along the tangent and normal unit vectors. The acceleration vector is always orthogonal to the binormal vector. The decomposition is...

I am wondering how can I find the infinitesimal displacement in any coordinate system. For example, in spherical coordinates we have the folow relations: x = \, \rho sin\theta cos\phi y = \, \rho sin\theta sin\phi z = \, \rho cos\theta And we have that d\vec l = dr\hat r +rd\theta\hat \theta...

Homework Statement If i want to show which direction is "positiv" I can do like this right? (Or is it wrong) 2. But if the figure would look like this, could i draw a coordinate system rather? Is this way to show which way i say as positive? or should i rather draw like this? Or Is...

This system of coordinates: can be "translated" in terms of x and y, so: x = \sqrt{\frac{\sqrt{u^2+v^2}+u}{2}} y = \sqrt{\frac{\sqrt{u^2+v^2}-u}{2}} Exist another form more simplified of write x and y in terms of u and v? I tried rewrite these expressions using the fórmulas of half angle but...

Homework Statement Transform the coordinates from the red c-system to the blue system. (Picture) Homework Equations Using(X Y) for the red cartesian system and (x y) for the blue system The Attempt at a Solution The solution to this problem gives x=Xcos▼ + Ysin▼ y=-Xsin▼+Ycos▼ Im not sure...

Homework Statement Show that the uvw-system is orthogonal. r, \theta, \varphi are spherical coordinates. $$u=r(1-\cos\theta)$$ $$v=r(1+\cos\theta)$$ $$w=\varphi$$ The Attempt at a Solution So basically I want to show that the scalar products between \frac{\partial \vec{r}}{\partial u}...

This is a very basic question, but what type of coordinate system is this? When is it useful to use? er, eθ, eΦ sinθ

The point P rotates with angle α to point P'. the coordinates of the old P are x1 and x2 and for P': x'1 and x'2. Prove that: $$x'_1=x_1\cos\alpha+x_2\sin\alpha$$ $$x'_2=x_2\cos\alpha-x_1\cos\alpha$$ I drew on the left the problem and on the right my attempt. the line OA, which is made of...

Homework Statement Our teacher said we can NEVER do an F=ma problem from an accelerating, or noninertial frame. (He said there are ways to do it, but we can not do it in his class), and I'm confused becuase often times he makes the "system" or makes a "free-body diagram" around an accelerating...

Suppose a position vector v is rotated anticlockwise at an angle ##\theta## about an arbitrary axis pointing in the direction of a position vector p, what is the rotation matrix R such that Rv gives the position vector after the rotation? Suppose p = ##\begin{pmatrix}1\\1\\1\end{pmatrix}## and...

Consider a line charge with charge density λ and a electric charge q. A coordinate system moving at velocity v ,it will see the line charge as a current ,and the electric charge(which is also moving seen from the moving coordinate system) will feels magnetic force. Why does this happens?

Hello, firstly I have to make the usual apologies of ignorance and inexperience, but that's why I'm here! I have a library of XML files which each contain two sets of image data. Together they make something very similar to this:http://imgur.com/vjs7MRH The grey and red points are given in...

Suppose we have a block on an inclined plane. If we choose the x-y axis to be parallel and perpendicular to the inclined plane, then we have Fy = N - mgcos30 = 0 But if we choose our trivial x-y coordinate system, where y is parallel to the force of gravity, then we get: Fy = Ncos30 - mg =...

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

The spectral radiance of a blackbody has units of W·sr-1·m-2·Hz-1. How do I deal with these units if I want to think about a 2D problem of radiation in Cartesian coordinates? I assume that instead of a sphere of emission (which would result in artificial decrease in intensity with the inverse...

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 =...

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...

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 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...

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...

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...

Homework Statement Two coordinate systems xyz (…fixed) and x0y0z0 (moving) coincide at time t = 0. The moving system is rotating about the …fixed z axis, which coincides with z0 axis. The angular velocity is given by ω = tk = tk0. The position vector as measured in the rotational frame is...

Can anyone explain very clearly(to a n00b like me) right ascension and declination and how to navigate to stars using this system?

Hello everyone, During my linear algebra, my professor had said that a true gentleman never picks a coordinate system, or something along those lines. He alluded to the person who said it, but I did not quite grasp who it was. I was wondering if anyone might know who said this. Thank you.

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

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...

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...

In Morse & Feshbach (P512 - 514) they show how 10 different orthogonal coordinate systems (mentioned on this page) are derivable from the confocal ellipsoidal coordinate system $(\eta,\mu,\nu)$ by trivial little substitutions, derivable in the sense that we can get explicit expressions for our...

I was checking the proof of this, when things came vague at one point. It goes as follows, how to prove that Lagrange's equations hold in any coordinate system? Answer: Let q_{a} = q_{a}(x_{1},..., x_{3N}, t) here the possibility of using a coordinate system that changes with time is...

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...