Coordinates Definition and 1000 Threads

is it logical to ask this question in Spherical coordinates: Using the differential length dl , find the length where r=1 0<Θ<∏/4 ∏/2< θ <∏/4 where Θ is the azimuthal angle. What I mean by ∏/2< θ <∏/4 is that the line is a "diagonal" line which has an ascention of ∏/4 from the xy...

First I would like to apologize first if this is the wrong place for posting this problem. I don't really understand what is the importance of w in the homogeneous coordinate (x,y,z, w). One of the example i have read is about a parrallel line extended to infinity, and both line would...

Give all the polar coordinates corresponding the rectangular point $$(-1, \sqrt{3})$$ Am i setting this up right? so would I use $$(r, \theta)$$ so $$x = rcos(\theta)$$ $$y = rsin(\theta)$$ $$r^2 = x^2 + y^2$$ so: $$(-1)^2 = (-1*\frac{2\pi}{3})^2 + (-1*\frac{11\pi}{6})$$ ?

Find the curve coordinates of the point nearest to P in the curve 5x2 -6xy +5y2 = 4 P = (0,0) oK x2 + y2 =D2 But how can i solve for x or y ? Maybe by expliciting derivative

I don't understand why I am screwing this up so bad. Sketch the graph of the equation $$r = 2 + 4cos(\theta)$$ in polar coordinates. So I did: $$0 = 2 + 4cos(\theta) $$ $$= -\frac{1}{2} = cos(\theta)$$ Then got $$cos(\theta)$$ is $$-\frac{1}{2}$$ @ $$\frac{2\pi}{3}$$ and @$$ \frac{4\pi}{3}...

Hi everyone, I've some points I want to make sure of. 1- When converting a "POINT" from a coordinate system to another, I'll just use the derived equation to convert (e.g. (1,2,3) from cartestian to cylindrical: \rho=\sqrt{x^{2}+y^{2}}, \phi=tan^{-1}\frac{y}{x}, z=z 2- When converting an...

I see a number of gravitational wave analytic solutions with the metric given in terms of Rosen coordinates. I have no idea what these coordinates are. How do I perform a coordinate transformation from Rosen coordinates to traditional (t,x,y,z) Euclidean\Cartesian coordinates? Also, is there a...

Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r < 0 so I did $$\frac{\pi}{3} + 2\pi = \frac{7\pi}{3} \therefore$$ $$r > 0$$ and did $$\frac{\pi}{3} + \pi = - \frac{4}{3} \pi$$ $$\therefore$$ $$r < 0$$...

Homework Statement First off, I am not a physics student. I am a math major taking a maple software course and there is a question that I can not figure out. The question gives me a radial coordinates r r:= \frac{a*t^{2}*e^{-b*t}}{1+t^{2}} And angular coordinates: θ:=b+c*t^{2/3} Where...

To write the uniform charge density of a disk with radius a in cylindrical coordinates, If we do this form: \rho (x)=\frac{A\delta(z)\Theta (a-\rho)}{\rho} (A is constant that sholud be determined and \theta is step function), we get A=\frac{Q}{2\pi a} and so: \rho (x)=\frac{\frac{Q}{2\pi...

Thank you for taking time to read my post, I hope I am putting into the correct area of the physics forum. I am working with a programmer to complete a project that involves 2 intersecting vectors and a circle. The vector coordinates are known, we are trying to solve the circle equation...

First, I'd like that you read this littler article (http://mathworld.wolfram.com/NaturalEquation.html). The solution given by Euler that coonects the system cartesian (x, y) with the curvature κ of the "cesaro system" (s, κ), is that the derivative of the cartesian tangential angle φ* wrt arc...

In the wiki, there is an explanation for what is the tangential angle in cartesian and polar coordinates. However, the orientation these angles aren't specified. In cartesian coordinates, I believe that the tangential angle φ is measured from the x-axis, in polar coordinates the tangential angle...

On the drawing below is a hexagonal lattice. For the basis vectors one can choose either the set of arrows in black or the set in yellow. The intersection coordinates of the plane in green seems to be the same regardless of choosing the black or the yellow basis. Why is that? My teacher said it...

My textbook says ψ(x,t)=exp(i(p_{0}x^{0} + p^{→}\cdotx^{→})/h)=exp(i*p\cdotx/h) (note that by h I mean 'h-bar'...couldn't find the symbol). I don't recognize (like my text implies I should) how the first equation equals the second. Where did the p_{0}x^{0} go? Sorry for my stupidity here. Any...

Homework Statement Image attached Homework Equations r2=x2+y2 The Attempt at a Solution ∫∫ re-r^2 drdΘ I'm not sure how to establish the boundaries. This is an online class so if you can offer any additional tips for evaluating types of integrals of this sort, that would be...

Note: physics conventions, \theta is measured from z-axis We have a vector operator \vec{L} = -i \vec{r} \times \vec{\nabla} = -i\left(\hat{\phi} \frac{\partial}{\partial \theta} - \hat{\theta} \frac{1}{\sin\theta} \frac{\partial}{\partial \phi} \right) And apparently \vec{L}\cdot\vec{L}=...

Hi everyone, I've two vectors in cylindrical coordinate - (-1,\frac{3\pi}{2},0),(2,\pi,1) - and I want to find the perpendicular unit vector of these two vector. Basically I'll use the cross product, then I'll find the unit vector by \hat{u}=\frac{\vec{u}}{||\vec{u}||}. But do you I...

I've been watching the Stanford lectures on GR by Leonard Susskind and according to him the metric tensor is not constant in polar coordinates. To me this seems wrong as I thought the metric tensor would be given by: g^{\mu \nu} = \begin{pmatrix} 1 & 0\\ 0 & 0\\ \end{pmatrix} Since...

Hello fellow PF go-ers I am having trouble with coordinates in curved space time lately, allow me to demonstrate my issue. Take the metric of flat space in spherical coordinates for example, a diagonal metric with values 1,r^2 and r^2sinΘ. It appears to me that only when we know that the Θ and...

Homework Statement Find the surface area of the Earth (as a fraction of the total surface of the earth) that lies above 50 degrees latitude North. Homework Equations $$A = \int_R\sqrt{|\det(g)|}d\theta d\phi$$ The Attempt at a Solution Hence I get $$\int_0^{360}...

Homework Statement In 3d coordinate space any two of the coordinate angles must A. Sum to less than one B. Be greater than ninety but less than one eighty. C. Each be greater than forty five degrees D. Sum to greater than 90 ( if they are both less than 90) E. Have cosines less than...

Hi, I have an involute gear and measured co-ordinates of two arbitrarily chosen points (on the involute portion) of a tooth. Can I find out the base circle with this information? Thanks.

Hellow everybody! If ##d\vec{r}## can be written in terms of curvilinear coordinates as ##d\vec{r} = h_1 dq_1 \hat{q_1} + h_2 dq_2 \hat{q_2} + h_2 dq_2 \hat{q_2}## so, how is the vectors ##d^2\vec{r}## and ##\vec{r}## in terms of curvilinear coordinates? Thanks!

I'm trying to implement a numerical code for the diffusion equation with moving boundaries. I have no problems with the numerical implementation, but with the transformation of coordinates. In spherical coordinates, the diffusion equation is \frac{\partial c}{\partial t} = D...

Homework Statement Find the corresponding rectangular coordinates for the point. (-2, \frac{5\pi}{3}) x = -2cos(\frac{5\pi}{3}) x = -2cos(\frac{2\pi}{3}) x = -2* \frac{-1}{2} = 1 y = -2sin(\frac{5\pi}{3}) y = -2sin(\frac{2\pi}{3}) y = -2*\frac{\sqrt{3}}{2} =...

For question 11 , how do you do part c? I know that (cos theta corresponds to x value and sin theta corresponds to y value. Using that I found the angle to be 318 degrees for part a. For part c, how would you start that? The answer is the coordinates flipped , x and y values with a positive...

Hi, Given 3D points P1(200,60,140), P2(300,120,110), P3(3,0,-1), P4(-100,0,-1) and the radius of arc C1MP3 is equal to radius of arc C2MP1. How do I calculate coordinates x, y, z of points C1 and C2? Points C1 and C2 are centers of two reverse arcs which are tangent to each other at point...

Hi, Given 3D points P1(200,60,140), P2(300,120,110), P3(3,0,-1), P4(-100,0,-1) and the radius of arc C1MP3 is equal to radius of arc C2MP1. How do I calculate coordinates x, y, z of points C1 and C2? See this image. Points C1 and C2 are centers of two reverse arcs which are tangent to...

Hellow! I have searched for some theory about linear system in polar coordinates, unfortunately, I not found anything... exist some theory, some book, anything about this topic for study? Thanks!

Hello, I am reading this paper on the casimir effect and I am failing to understand where the 1/(2âˆ)^2 comes in and how the polar coordinates are converted to Cartesian. The equations are (3.23) and (3.24). http://aphyr.com/data/journals/113/comps.pdf Thank you!

I was looking at the Wikipedia entry on the Hamilton-Jacobi equation, and was confounded by the equation at the beginning of the section on spherical coordinates: http://en.wikipedia.org/wiki/Hamilton–Jacobi_equation#Spherical_coordinates Shouldn't the Hamiltonian simply be $$ H =...

Hello, In Cartesian coordinates, if we have a point P(x1,y1,z1) and another point Q(x,y,z) we can easily find the displacement vector by just subtracting components (unit vectors are not changing directions) and dotting with the unit products. In fact we can relate any point with a position...

Homework Statement ∫∫√(x^2+y^2)dxdy with 0<=y<=1 and -SQRT(y-y^2)<=x<=0 Homework Equations x=rcos(theta) y=rsin(theta) The Attempt at a Solution 0.5<=r=1, we get r=0.5 from -SQRT(y-y^2)<=x by completing the square on the LHS then, 0<=theta<=pi But, when I calculated the...

1) If u(r,\theta,\phi)=\frac{1}{r}, is \frac{\partial{u}}{\partial {\theta}}=\frac{\partial{u}}{\partial {\phi}}=0 because u is independent of \theta and \;\phi? 2) If u(r,\theta,\phi)=\frac{1}{r}, is: \nabla^2u(r,\theta,\phi)=\frac{\partial^2{u}}{\partial...

Our professor's notes say that "In general, in Hamiltonian dynamics a constant of motion will reduce the dimension of the phase space by two dimensions, not just one as it does in Lagrangian dynamics." To demonstrate this, he uses the central force Hamiltonian...

Homework Statement Use polar coordinates to set up and evaluate the double integral f(x,y) = e-(x2+y2)/2 R: x2+y2≤25, x≥0 The Attempt at a Solution First I just want to make sure I'm understanding this my double integral would be ∫^{\pi/2}_{-\pi/2} because x≥0 ∫^{5}_{0}...

Homework Statement Use polar coordinates to find the volume of the given solid. Enclosed by the hyperboloid -x2 - y2 + z2 = 1 and the plane z = 2 Homework Equations r2 = x2 + y2, x = rcosθ, y = rsinθ ∫∫f(x,y)dA = ∫∫f(rcosθ,rsinθ)rdrdθ The Attempt at a Solution -x2 - y2 + 4...

So, I was curious about this and found more or less what I was looking for here: http://electron9.phys.utk.edu/vectors/3dcoordinates.htm Except, something is bothering me about those equations. At the very bottom, the equation for Theta in a spherical coordinate system; shouldn't it be...

Homework Statement x = eKcos(k) y=eKsin(k) -∞ < K < ∞ Find an equation in polar coordinates for the above curve The Attempt at a Solution I am not fully clear as to what the question is asking. If its asking for (r,k), where K is normally a theta value then it would be...

Homework Statement Evaluate the iterated integral ∫ (from 0 to 1) ∫ [from -sqrt(1-x^2) to sqrt(1-x^2) ] ∫ (from 0 to 2-x^2-y^2) the function given as √(x^2 + y^2) dz dy dx The Attempt at a Solution I changed the coordinates and I got the new limits as ∫(from 0 to pi) ∫(from...

Homework Statement Assume that f(x,y,z) is a continuous function. Let U be the region inside the cone z=√x^2+y^2 for 2≤x≤7. Set up the intregal ∫f(x,y,z)dV over U using cartesian, spherical, and cylindrical coordinates. Homework Equations CYLINDRICAL COORDINATES x=rcosθ y=rsinθ z=z...

I recently had to do an integral like the one in the thread below: http://math.stackexchange.com/questions/142235/three-dimensional-fourier-transform-of-radial-function-without-bessel-and-neuman The problem I had was also evaluating the product and I am quite sure that the answer in the thread...

convert $$r=5\sin{2\theta}$$ to rectangular coordinates the ans to this is $\left(x^2+y^2\right)^{3/2}=10xy$ however... multiply both sides by $r$ to get $r^2=5\cdot r \cdot \sin{2\theta}$ then substitute $r^2$ with $x^2+y^2$ and $\sin{2\theta}$ with $2\sin\theta\cos\theta$ and divide each...

I'm not sure whether this falls in the homework category, or the standard calculus section, so apologies in advance if this doesn't fall in the right category. Homework Statement Evaluate ∫∫∫e^[(x^2 + y^2 + z^2)^3/2]dV, where the region is the unit ball x^2 + y^2 + z^2 ≤ 1. (or any...

Homework Statement Convert ∫ from 0 to 3/√2 ∫ from y to √(9-y^2) of xydxdy to polar form. Homework Equations x2+y2=r2 The Attempt at a Solution I found the equation x2+y^2=9 from the upper range of the second integral. So r=3. Therefore r ranges from 0 to 3. The integrand is...

Homework Statement The problem states: Use cylindrical coordinates to evaluate \iiint_V \sqrt{x^2 +y^2 +z^2} \,dx\,dy\,dz where V is the region bounded by the plane z = 3 and the cone z = \sqrt{x^2 + y^2} Homework Equations x = r cos( \theta ) y = r sin( \theta ) z =...

Dear, I have a task to model the behaviour of certain interphase material. Let's say that functions which describe the change of material parameters are known. i.g. change of the Young's modulus as function of distance from neighbouring material (or (0,0) origin) - PAR=PAR(x)...

Homework Statement Convert (1,-2) to polar coordinates find one representation with r >0 and one with r <0. Also 0<= theta <= 2 PI Homework Equations I used tantheta = y /x , and x^2 +y^2 = r^2 The Attempt at a Solution I got (sqrt(5) , arctan(-2)) , (-sqrt(5) , arctan(-2) + pi...

i'm trying to integrate some some function bounded by the x-y domain of x2+y2=6y which is a circle on the x-y plane shifted upward where the outer part of the circle is 6. i'm trying to integrate a double integral.. ∫∫f(x)rdrdθ i don't know how to express my limits of integration for r...