Coordinate Definition and 910 Threads

Homework Statement r(t)={sin(pi*t),ln(t),((1/4)e^t} At what time(s) does the object intersect one of the coordinate axes? At what time(s) does the object intersect one of the coordinate planes? During what times t is the object in the first octant? Homework Equations Not...

While not paying attention in class my friend made a joke that a cube squared was in six dimensions, or something like that. Terrible joke, but now I'm trying to figure out if it is valid to arithmatically combine the basis vectors for two or more coordinate systems to get a new one.

I have seen in various locations different conventions regarding the location of a prime symbol denoting a tensor represented in a new frame. For example, if the position four-vector is x^{\mu} then this four-vector in a different frame is often written as either x'^{\mu} or...

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...

Main question: What is the name of the 8 coordinate complex pointgroup? Or does it even exist? I've been exposed to octahedrons and icosohedrons, however, the 8 coordinate high symmetry complexes appear to have been skipped. I'm aware that these complexes would be rare but I think that...

Homework Statement You're tracking a plane from the ground. The plane is at a constant height h from the ground, at a distance r from you at the illustrated instant, and at an inclination theta. The plane's speed is constant at 1200km/hr. Find the rate at which your tracking dish must rotate...

Homework Statement For the cartesian, cylindrical, spherical coordinate system, prove that \nabla.\vec{r} = 3 and \nablax\vec{r}=0 Homework Equations For cylindrical coord system, \vec{r} = s\vec{s} + z\vec{z} \nabla = \vec{s} \delta/\deltas +...

Why use a tensor density transformation when doing a coordinate transformations? What is the advantage? I've always learn that transforming a tensor involves pre and post multiplying by the transformation tensor and it's inverse respectively, but I've come across ones in my research that use...

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}...

I've studied classical physics and never heard this before until recently...the allowable coordinate transformations for classical mechanics are rotations and translations. Could someone explain why this is so? What makes these "allowable" (I know they are orthogonal transformations).

so i know for example that d/dt (∂L/∂x*i) = ∂L/∂xi for cartesian coordinates, where xi is the ith coordinate in Rn and x*i is the derivative of the ith coordinate xi with respect to time. L represents the lagrangian. so using an arbitrary change of coordinates, qi = qi(x1, x2, ..., xn) i...

What does it mean for a vector to remain "invariant" under coordinate transformation? I think I already know the answer to this question in a foggy, intuitive way, but I'd like a really clear explanation, if someone has it. I know all of multivariable calculus and quite a bit of linear algebra...

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

Homework Statement Prove this equation Homework Equations The Attempt at a Solution I almost get the answer. But I don't know why all of the sin and cos are in reciprocal form.

find the volume of the solid D that lies above the cone z = (x^2 + y^2)^1/2 and below the sphere z = (x^2 + y^2 + z^2) i've done the integration until i need to substitute cos phi = u.. however.. i don't know to change the range.. http://imageshack.us/photo/my-images/839/spherical.jpg/"

Before I ask the question, let me remind that desargues theorem states : if two triangles are perspective from one point then they are perspective from one line I'd like to ask whether the order of the steps of the proof I did is correct or not. Since I saw the proof from an article but it...

Hey there.. i try to solve the question below.. but.. i still didn't get the answer given by my lecturer.. the answer should be.. pi/4(e - 1) where did i do wrong? http://imageshack.us/photo/my-images/215/06072011697.jpg/ http://imageshack.us/photo/my-images/17/06072011699.jpg/...

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...

In the derivation of the Eddington-Finkelstein coordinates in Schwarzschild spacetime we started with the worldline of a radially ingoing photon: ct=-r-2mln(\frac{r}{2m}-1)+C where C is a constant of integration since we got this from integrating the dt/dr with negative sign from the...

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...

1. Calculate the coordinate of a triangle's 3rd corner when 2 corner coordinates and area is given (in Surveying). Given: Area of triangle ABC = 14994sqm Corner B coordinate = +3541.620 (Y); -5467.650 (X) Corner C coordinate = +3300.580 (Y); -5503.150 (X) Calculate corner A's coordinates? I...

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...

I was wondering, if a metric known to be a solution of Eintein field equation can be a static or expanding spacetime depending on a change of coordinates, what does this tells us about that metric? Can it be physical? I mean in the sense that it is usually said that to check if something is...

Find the change of coordinate matrix from\gamma coordinates to \beta coordinate where \beta is the standard basis for P2(R) and \gamma={ 1+t^2, t-t^2, 1-2t +t^2} Since i can't figure out how to type matrices i will explain what I did. I made a 3 by 3 matrix and put the \beta basis on the...

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

Homework Statement Find the area enclosed by the curves: r=\sqrt(3)cos(\theta) and r=sin(\theta) Homework Equations The area between two polar curves is given by: A=(1/2)\int{R^2 - r^2dr} where R is the larger function and r is the smaller function over an interval. The Attempt at a...

Homework Statement An ant walks from the inside to the outside of a rotating turntable. Write down it's velocity vector. Use polar the cartesian coordinates. Homework Equations I have already derived the velocity vector in polar coordinates which is: \hat{v} = \dot{r}\hat{r} +...

The title pretty much says it. According to my book, Classical Dynamics by Thornton and Marion, generalized coordinates can be quantities other than position such as energy or length squared, but what about time?

Hello, I am trying to understand this partially rotated coordinate systems. I do not understand how does x'=xcos(theta)+ysin(theta) and y'=ycos(theta)-xsin(theta) I am probably stuck at silly answer but i need this to understand deriving of formulas for special relativity. Thanks

Hi, I am trying to simulate a freely jointed chain polymer to do that I want to put several rods (length a) on top of each other but with different angles. My problem is like this I have a vector(1) and at the end of this vector(1) I put another vector(2), the z-axis of this vector(2)'s...

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...

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...

Given a surface of positive curvature embedded in R^3 choose coordinate charts around each non-umbilic point so that the cross terms in both the first and second fundamental forms are zero. These are coordinates where the tangents to the coordinate axes point in the direction of the...

Hello! When using the Schwarzschild exterior metric in the klein-gordon equation one can perform the standard tortoise(E-F) coordinate transform to yield a wave equation which has a well defined potential that is independent of the energy term. My understanding is that the motivation for this...

Hi there, Physics lovers. I'm studying "The Classical Theory of Fields" from the "Course of Theoretical Physics" book series by Lev D. Landau, and I'm stuck with simultaneity in General Relativity. In page 251 of the Fourth "revised" english edition, by Butterworth Heinemann, There begins the...

Hi everyone, Given two different reference frames in a vector space; say left and right. v is a vector defined in the left frame and u is a vector defined in the right frame. What is the nature of a matrix A that can satisfy the equality u= A.v? Thank you

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...

Calculus: Coordinate Changes, Jacobian, Double Integrals?? Homework Statement Show that T(u,v) = (u2 - v2, 2uv) maps to the triangle = { (u,v) | 0 ≤ v ≤ u ≤ 3 } to the domain D, bounded by x=0, y=0, and y2 = 324 - 36x. Use T to calculate ∬sqrt(x2+y2) dxdy on the region D...

hey, I know this might be abit silly, but u know the cauchy-reimann formula for a complex function to be diffrentiatable? here is a link to what I am talking about: http://en.wikipedia.org/wiki/Cauchy-Riemann_equations my question is: how do I write it in polar coordinates?:redface:

Hi, My question is the following. In special relativity, the Lorentz transformations correspond to a physical situation in which two frames of reference move with uniform rectilinear motion one with respect to the other. In general relativity, given the physical situation in which one frame...

For a defect in a semiconductor. We plot the energy against some "configuration coordinate", noted in general as "Q". What is this coordinate ? In my understanding it is some position related to the defect in question. Also, is the energy plotted in the diagram the energy of the...

Given a set of 2D coordinates (real numbers, involves positives and negatives), I could calculate the (weighted) barycenter by simply using the logic with plain numbers. For the barycenter calculations, I sum all the values with respect to x-axis and y-axis separately, and then divide with the...

Homework Statement Please help me graph this on xyz coordinate plane A golfer strikes the ball of the tee at x=0;y=0;z=0. The hole center is located at a distance of 150m north(+x) and 75m west(+y) of the tee. The upper edge of the hole is 10m below(-z) the height of the tee. If the the...

Homework Statement A regular tetrahedron has the vertices of its base A(1,1,0) B(3,1,0) C(2,1+(3^(1/2),0). Find coordinate of vertex S? Homework Equations The Attempt at a Solution If this is a tetrahedron Then we know the length by caclulating the distance formula, which gives...

Hi, I am reviewing some vector calculus and have a problem on the derivation of the divergence in the spherical coordinate. Assume there is a small volume located at r_0, \theta_0, \phi_0 with a volume of r_0^2\sin\theta_0 \Delta r \Delta \theta \Delta \phi. My question is that why...

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...

In an earlier thread, I asserted that a rod has one true length, its rest length. If so, then the shorter coordinate length which is measured in some other frame must be somehow untrue. In this thread I argue that the coordinate length is a distorted view of the true length. In the graphic...