Coordinates Definition and 1000 Threads

Hi, When I do the following transformation: $$ X_1=x_1+x_2 \\ X_2=x_2 $$ It turns out that the Jacobian ##\partial (X_1,X_2)/\partial (x_1,x_2)## is 1. But we have: $$ dx_1dx_1+dx_1dx_2=d(x_1+x_2)dx_2=dX_1dX_2=|\partial (X_1,X_2)/\partial (x_1,x_2)|dx_1dx_2=dx_1dx_2 $$ So we...

There is a circular gate rotating at a constant angular speed of ω. The circular gate has a tunnel across its diameter. The mission is to pass through the gate. (That is, come in one side of the gate, travel the whole diameter, and exit at the other side.) Also, craft is neutrally buoyant...

According to the Schwarzschild solution in the most common anisotropic (Schwarzschild?) coordinates the proper time and the coordinate time are related as...

Hello all i have a question about adding 3 impedances given in polar form, must i convert them to x..y.. first or is there a quicker way on a calculator and if so can anyone give advice i have the equation Zo=√Z(oc)Z(sc) but finding it hard to understand many thanks.

I have a grid and want to determine whether a point lies within (our outside of) a circle. The grid cells simply have integer coordinates, e.g. x = 5, y = 7. The circle's radius is known, and also an integer value. I wrote a program that can place points in a (quantized) circle using...

Consider a regular hexagon ABCDEF (in order counterclockwise). Determine the coordinates of AB, AE AND AF (->) in the base (AC, AD) (->) AB(->)=(_____,_____) AE(->)=(_____,_____) AF(->)=(_____,_____) what I mean with exemple AF(->) positive way from A to F. I have draw a it but I got problem...

Homework Statement "You are now going to show that, in the Gaussian distribution P(x)=Ae^(-Bx^2) the constant A is equal to sqrt(B/Pi). Do this by insisting that the sum over probabilities must equal unity, Integral(P(x)dx)=1. To make this difficult integral easier, frst square it then combine...

Homework Statement Find two other pairs of polar coordinates of the given polar coordinate, one with r > 0 and one with r < 0. Then plot the point. (2, 5π/3)Homework Equations I don't there are any. The Attempt at a Solution I'm not completely sure of how to do this actually. I know that...

I've done this problem and I have a feeling it's incorrect. I've never done a problem like this so I am kind of confused on how else to go about doing it. The goal is to change the cartesian integral $$\int_{-a}^{a}\int_{-\sqrt{a^2-x^2}}^{\sqrt{a^2-x^2}}\,dy\,dx$$ into an integral in polar...

Homework Statement I am currently trying to prove: S = ∫∫a2sinΦdΦdθ Here is my work (note that in my work I use dS instead of S, this is an accident): I end up with: S = ∫∫a*da2sinΦdΦdθ Where da is the infinitesimal thickness of the surface. Why am I getting the wrong answer?

Homework Statement The 2-oz bead P is given an initial speed of 5 ft/sec at point A of the smooth guide which is curved in the horizontal plane. The horizontal force between the bead and the guide has a magnitude of 3 oz at point B. Determine the radius of curvature ρ of the path at this...

Homework Statement Evaluate the integral using polar coordinates: ∫∫arctan(y/x) dA Where R={ (x,y) | 1≤ x2 + y2 ≤ 4, 0≤y≤x Homework Equations X=rcos(T) Y=rsin(T) r2=x2 +y2 The Attempt at a Solution First thing was drawing a picture of R, which I think looks like a ring 1 unit thick...

Hello all, I've been puzzled by this problem for some time now and was wondering if anyone here could help me out. Textbooks on GR (specifically when going into gravitational waves) tend not to elucidate this. It's often taken for granted that through the gauge diffeomorphism invariance (or...

Homework Statement Use cylindrical coordinates to describe the line through the point (1,1,0) and parallel to the z-axis. Homework Equations How does one go about this? Even my course book was unclear about this. Any general overview about how to do such a question will be helpful. The...

Hey, folks. I'm trying to derive the surface area of a sphere using only spherical coordinates—that is, starting from spherical coordinates and ending in spherical coordinates; I don't want to convert Cartesian coordinates to spherical ones or any such thing, I want to work geometrically...

Homework Statement Derive the expression for kinetic energy of a classical particle in spherical coordinates. Homework Equations I believe the answer I am supposed to reach is: T=\frac{1}{2} m (\dot{r}^2 + r^2\dot{\theta^2} + r^2\dot{\phi ^2}sin^2\theta) The Attempt at a Solution...

Homework Statement Find the exact coordinates of the centroid for the region bounded by the curves x=5-y^ 2 and x=0 I am not sure about this one because it uses dy instead of dx i think. I tried to set it up like this x= [0.5∫(5-y^2)^2 dy from -5 to 5]/[ ∫(5-y^2)dy from y=-5 to 5]...

Homework Statement Given \int^{\sqrt{6}}_{0}\int^{x}_{-x}dydx, convert to ploar coordinates and evaluate. Homework Equations We know that x=rcos\theta and y=rsin\theta and r =x^2+y^2 The Attempt at a Solution First, I defined the region of the original integral: R = 0...

Homework Statement Find the coordinates of the point(s) on the following curves where the second derivative is as stated. Homework Equations y= \frac{x^3}{12} and \frac{d^{2}y}{dx^{2}} = 1.5 The Attempt at a Solution I'm used to working with the first derivative. Would I need to...

How do I transform my x, y values into screen coordinates system All values is in pixels In my coordinate system origo is located in (40,495) The display area that I can use is from X=40 to x=750 and from y=495 to y=55 When you go down in the coordinate system the y value is increasing...

I can't provide all the information, because I'm on my mobile phone. Here is a shot of the problem: The tangent of each curve is the slope, right? So how do we use that to find vf (instantaneous velocity) at 4s and 8s

I'm reviewing math material for the EIT exam, I'm going over math concepts that should be pretty basic but I feel like there are gaps in my understanding. I understand how we can use rectangular coordinates and complex numbers to find a point on the complex plane. It would follow logically...

Dear all, I am reading R.A. Sharipov's Quick Introduction to Tensor Analysis, and I am stuck on the following issue, on pages 38-39. The text is freely available here: http://arxiv.org/abs/math/0403252. If my understanding is correct, then the Jacobi matrices for the direct and inverse...

[FONT=arial]A circle is drawn through the focus of the parabola $2a/r=1+ \cos( \theta)$ to touch it at the point $\theta=\alpha$. Find the eq. of the circle in polar form. [FONT=arial]Please help

I've been working through Polchinski on my own, and I have a really basic question. How would one derive equation 2.4.1? What does it even mean to write the stress tensor with the new indices z and z-bar? I thought this was obvious, but it isn't working out for me.

I am trying to understand Rindler coordinates at a basic level. Here is what I have so far: A uniformly accelerated observer will follow a hyperbolic path in a stationary frame. This is equivalent to having a stationary observer in a uniformly accelerated reference frame. This where...

Homework Statement In the attachment, I do not understand how we got the second equation in terms of polar coordinates. Homework Equations The Attempt at a Solution I tried doing it by writing z_dot = (...)z and then plugging in r* exp i theta, but to no avail.

Hi all. Is there a way to plot both functions and coordinates/points on the same graph in Mathematica? The various functions for plotting each seem very incompatible. I would like to compare a probability function to Monte-Carlo-method simulation results. Also, out of curiosity, do...

I have a uniform grid of data in spherical coordinates. e.g. theta = 0, 1, 2, ... 180 and phi = 0, 1, 2, ... 359 which forms a 2D matrix. I wish to rotate these points around a cartesian axis (x, y, z-axis) by some angle alpha. To accomplish this I currently do the following: 1. Convert to...

Homework Statement Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is bounded by the parabolas y = x^2 and x = y^2; ρ(x, y) = 23√x Homework Equations m = \int\int_{D} ρ(x, y) dA x-bar = \int\int_{D} x*ρ(x, y) dA y-bar =...

Homework Statement Prove the La Placian of V(x,y,z)=(zx^{2})/(x^{2}+y^{2}+z^{2}) in Cartesian coordinates is equal to that in Spherical coordinatesHomework Equations \nabla^{2}V=0 The Attempt at a Solution I have attempted to calculate all the terms out, and there were A LOT. I was hoping...

The question is: Using the chain rule to prove that a function $f:\mathbb{R}^n\rightarrow \mathbb{R}$ which is polynomial in the coordinates is differentiable everywhere. (The chain rule is for the use under function composition circumstances, how to apply it here to prove that the function $f$...

Homework Statement Find the volume of the solid that lies between z=x2+y2 and x2+y2+z2=2 Homework Equations z=r2 z=√(2-r2) The Attempt at a Solution So changing this into cylindrical coordinates, I get z goes from r2 to √(2-r2) r goes from 0 to √2 theta goes from 0...

Is it possible to use celestial coordinates which were taken 50 years ago? What kind of inaccuracy can we expect (give the answer in degrees)? Could I say that it will be about 0.3° error assuming that around the year 130 BC, Hipparchus compared ancient observations to his own and concluded that...

Homework Statement A point is chosen randomly in the interior of an ellipse: (x/a)^2 + (y/b)^2 = 1 Find the marginal densities of the X and Y coordinates of the points. Homework Equations NA The Attempt at a Solution So this ought to be uniformly distributed, thus the density function...

Homework Statement "The shortest path between two point on a curved surface, such as the surface of a sphere is called a geodesic. To find a geodesic, one has to first set up an integral that gives the length of a path on the surface in question. This will always be similar to the integral...

hello i am solving heat equation in cylindrical coordinator. i am using MATLAB "pdepe" solver to solve the partial differential equation. can anyone suggest me how to choose the initial condition?

Homework Statement A particle moves with constant speed v around a circle of radius b. Find the velocity vector in polar coordinates using an origin lying on the circle. https://www.desmos.com/calculator/maj7t9ple1 Imagine the r starts at (0,0). Homework Equations \frac{d\vec{r}}{dt} =...

Homework Statement Write the vector expression for the acceleration a of the mass center G of the simple pendulum in both n-t and x-y coordinates for the instant when θ = 66° if θ'= 2.22 rad/sec and θ"= 4.475 rad/sec2 I have attached an image of the question. Homework Equations an =...

Find the volume of a cone with radius R and height H using spherical coordinates. so x^2 + y^2 = z^2 x = p cos theta sin phi y= p sin theta sin phi z= p cos phi I found theta to be between 0 and 2 pie and phi to be between 0 and pie / 4. i don't know how to find p though. how...

Hi all, Del = i ∂/∂x + j ∂/∂y + k ∂/∂z in x y z cordinate similarly I require to see the derivation of del in other coordinates too. Please give me a link for the derivation.

Large, cylindrical bales of hay used to feed livestock in the winter months are D = 2 m in diameter and are stored end-to-end in long rows. Microbial energy generation occurs in the hay and can be excessive if the farmer bales the hay in a too-wet condition. Assuming the thermal conductivity of...

Homework Statement http://i277.photobucket.com/albums/kk63/lioricsilver/Untitled_zps7cf41f04.png Homework Equations y2=(16)x is the equation on the question The Attempt at a Solution I have got any clue. I do know how to solve motion in 2d. But since time is not given or the...

I'm trying to convert the below Cartesian coordinate system into cylindrical and spherical coordinate systems. For the cylindrical system, I had r,vector = er,hat + sint(e3,hat). While I do have a technically correct answer for the spherical coordinate system, I believe, I was wondering if there...

Homework Statement Find the volume of the solid that the cylinder r = acosθ cuts out of the sphere of radius a centered at the origin.Homework Equations Cylindrical coordinates: x = rcosθ, y = rsinθ, z=z, r2 = x2+y2, tanθ = y/xThe Attempt at a Solution So I know that the equation for the sphere...

Homework Statement Show that: I = \int\int_{T}\frac{1}{(1 + x^{2})(1 + y^{2})}dxdy = \int^{1}_{0}\frac{arctan(x)}{(1 + x^{2})}dx = \frac{\pi^{2}}{32} where T is the triangle with successive vertices (0,0), (1,0), (1,1). *By transforming to polar coordinates (r,θ) show that:* I =...

Homework Statement The quality of the image is bad so here's the statement: For an interval of motion the drum of radius b turns clockwise at a constant rate ω in radians per second and causes the carriage P to move to the right as the unwound length of the connecting cable is...

Homework Statement It's given that absolute permitivity is a coordinate function: ε (x, y, z) = Asin(x)cos(y), where A=const Homework Equations We need to find an electrostatic field potential function \varphi in Cartesian coordinate system. The Attempt at a Solution I tired to solve, but...

Homework Statement The following equation describes a straight line: ⟨x, y, z⟩ = ⟨−1, 0, −2⟩ + t⟨1, 2, 2⟩ Find the coordinates of the point where this line intersects the y-axis. Homework Equations Equation of a Line: r = ro + tv The Attempt at a Solution I'm not really sure...

Homework Statement I know I have the set up done correctly I am wondering where I went wrong because I know I cannot get zero, and I am a little worried I did my integration wrong. please help. http://i1341.photobucket.com/albums/o745/nebula-314/IMAG0107_zps3cde35a8.jpg