Coordinate Definition and 868 Threads

Homework Statement Given that P,Q and R lie on the hyperbola xy=c2, prove that if PQ and PR inclined equally to the coordinate axes, then QR passes through O. Homework Equations The Attempt at a Solution I don't understand what does ''PQ and PR are inclined equally to the...

Me and my friend have been arguing about the coordinate system used for the earth... specifically gravity. he's trying to tell me the value of gravity is -9.8ms/2, when I've read from several books and other online resources that's it 9.8ms/2... a positive number. Hes keeps going on and on and...

Homework Statement 2 circles have the equation x2+y2-2x-2y+1=0 and x2+y2-12x-12y+36=0 respectively. Both circle touches the x-axis, y-axis and the line 3x + 4y = 12. Find the fourth tangent of the 2 circles. Homework Equations The Attempt at a Solution This is second part of the...

Homework Statement A variable point P lies on the curve y2 = x3 and is joined to a fixed point A with coordinate (2,0). Prove that the locus of the mid-point of AP is y2= 2(x-1)3. Homework Equations The Attempt at a Solution According to what i know, I need to know the...

Homework Statement Homework Equations F=ma vi=vf + at The Attempt at a Solution If i was to define upward as positive y direction, would the answer be = -881 pounds (btw why is the answer in the image in Newtons?) and because i defined upward as +y would ƩF = T - w? where w = mg.

Homework Statement Prove that the coordinates of a vector v in a vector space Vn are unique with respect to a given basis B={b1,b2,...,bn} Homework Equations The Attempt at a Solution not sure at all what to do with this

Homework Statement http://imageshack.us/photo/my-images/703/dfdfu.jpg Homework Equations To find the x coordinate 1. Make both equations equal, expose e and take logs. I'm not sure how to do this and I've tried but keep getting the wrong answer. 2. To find the area, subract the...

Question - Regarding a cnc cmm controller, What is tunneling? How is this measured? What impact does the cmm structure have on this characteristic?

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 Find dy/dx and determine the exact x coordinate of the stationary point for: (a) y=(4x^2+1)^5 (b) y=x^2/lnx Homework Equations The Attempt at a Solution (a) y=(4x^2+1)^5 dy/dx=40x(4x^2+1)^4 40x(4x^2+1)^4=0 Find x... How? (b) y=x^2/lnx...

Homework Statement How does ∂aAb behave under coordinate transformations in special relativity? Work out ∂'aA'b Homework Equations The Attempt at a Solution I have been given back the solution sheet to this problem, but I don't understand it. This is what I have I get...

Homework Statement Use polar coordinates to compute the volume of the region defined by 4 - x^{2} - y^{2} ≤ z ≤ 10 - 4x^{2} - 4y^{2} Homework Equations The Attempt at a Solution I got z = 2 so set up the equation V = f^{2pi}_{0}f^{5/2}_{2}f^{0}_{2}r*dzdrdθ is the domain...

Homework Statement f(x,y) = e^{x^2+y^2} x^{2} + y^{2} ≤ R Homework Equations The Attempt at a Solution I believe this is a circle. f^{2pi}_{0}^{sqrt(R)}_{-sqrt(R)}e^{x^2+y^2}*r*dr*dθ = f^{2pi}_{0}f^{sqrt(R)}_{-sqrt(R)}e^{r^2}*r*dr*dθ after u substitution... =...

Homework Statement f(x,y) = y(x^{2} + y^{2})^-1 y ≥ \frac{1}{2}, x^{2} + y^{2} ≤ 1Homework Equations The Attempt at a Solution Would you check my domain please? f^{pi}_{0}f^{sqrt(3)/2}_{-sqrt(3)/2} sinθ drdθ

Homework Statement f(x,y) = xy x ≥ 0, y ≥ 0, x^{2} + y^{2} ≤ 4 Homework Equations The Attempt at a Solution f^{pi/2}_{0}f^{2secθ}_{0} rcosθ * rsinθ * r drdθ I just wanted to check... is this right?? because I really don't think it is

Homework Statement Alright, here's the question, A stream function for a plane, irrotational, polar-coordinate flow is ψ=9r^2sin^θ. Find out the velocity potential in Cartesian Co-ordinate! Homework Equations The Attempt at a Solution Well, I can easily find out the velocity...

Through my mathematical fumblings, I think I have found a metric which gives a solution of the geodesic equation of motion that is asymptotic. It is a diagonal metric, with g00 = (x_1)^(-3) and g11 = 1. I am largely self-taught with SR so I may be miles off, but I think this gives a G.E. of M...

today in my physics course we were using jacobians to transform coordinate systems. This made me wonder if there was a way of deriving an optimal coordinate system to use for a given problem. -optimal meaning most simplified equation of a surface or bounds of a constraint (ex. cylindrical...

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 the problem the book the book chose to use the axis in the left diagram... but why can you not use the coordinate axis from the right diagram?

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} &...

curvilinear coordinate systems and "periodic" coordinates Hello, we can consider a generic system of curvilinear coordinates in the 2d plane: \rho = \rho(x,y) \tau = \tau(x,y) Sometimes, it can happen that one of the coordinates, say \tau, represents an angle, and so it is "periodic"...

I am confused how they picked the direction right of block M1 to be -x and the downward direction of block M2 to be +x..? I didn't know that one could create two different coordinate axis. Correct me if I am wrong but it seems that if you are working with two diff body's that are not in...

Homework Statement I'm having trouble understanding coordinate transformations for vector fields. There are two 'coordinate pieces', the coordinates pieces of the vector at a point changes, and the function describing the field can also be rewritten in terms of the new coordinates. I'm...

So I have the following shape for which I want to calculate the inertia matrix. Basically I just want to know what limits of integration I should use if I am using spherical coordinates. Assume the convention that phi is the angle from x to y in the xy plane and theta is from z to the xy plane...

How do you find these on the unit circle: 5pi/2 ? howabout pi/8 ? Converting from polar to rectangular? It says convert (-1, pi/8 ) from polar to rectangular coordinate? But there is no pi/8 on the unit circle? If the'yre on the unit circle just use x=rcosθ and y=rcosθ another example is for...

I'm trying to follow the math in Wald's General Relativity where he starts out with the equation for covariant derivative: \nablab\omegac = \partialb\omegac - \Gammadbc\omegad He uses that to derive the equation for a double covariant derivative: \nablaa\nablab\omegac =...

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...