Spherical coordinates Definition and 351 Threads

I am looking for ideas on how to solve this equation: \nabla \cdot \left( \vec{A} + F \hat{b} \right) = 0 where \vec{A} and \hat{b} are known vectors of (r,\theta,\phi) and F is the unknown scalar function to be determined. Also, \nabla \cdot \hat{b} = 0. So the equation can also be expressed...

Homework Statement (a) For spherical coordinates, show that \hat{\theta} points along the negative z-axis if \theta = 90°. (b) If \phi also equals 90°, in what direction are \hat{r} and \hat{\phi}?Homework Equations The Attempt at a Solution can i just explain this in words.. like for a...

Should be quite easy, really, given that it's just adding things together, hey ho. Problem a position vector of point (1), identified by sherical coordinates, is 5m away from point (2). I have a unit vector R1,2 identified by spherical coordinates [Aex - Bey +Cez], giving the direction to...

Hello everyone, I recently tried to find the surface area of a hollow cone (there is no base, like an ice cream cone) using spherical coordinates. With cylindrical coordinates I was able to do this easily using the following integral: \int \int \frac{R}{h}z \sqrt{\frac{R^{2}}{h^{2}} + 1}...

Homework Statement http://img28.imageshack.us/img28/7118/capturenbc.jpg Homework Equations x2 + y2 + z2 = p2 http://img684.imageshack.us/img684/3370/eq0006m.gif The Attempt at a Solution Using the relevant equations I converted the given equation to: ∫∫∫e(p3/2) * p2 *...

Homework Statement Here is the question given: Homework Equations The Attempt at a Solution So i set p as x^2 + y^2 + z^2 so p lies in between b and a. But how do i find the restrictions on the two angles, theta and phi?

[b]1. Find the work done by the force F=r3*cos2\varphi*sin\varphi*\hat{r} + r3*cos\varphi*cos(2\varphi) \hat{\varphi} from the point (0,0,0) to (2,0,0) Homework Equations Work=\int F*dr where dr= dr\hat{r} + rd\varphi\hat{\varphi}The Attempt at a Solution When muliplying the line element, dr...

Homework Statement I want to derive the square of the total angular momentum as shown here: http://en.wikipedia.org/wiki/Angular_momentum_operator#Angular_momentum_computations_in_spherical_coordinates Homework Equations The x,y, and z components of angular momentum are shown in the...

Homework Statement a.) Set up the Lagrange Equations of motion in spherical coordinates, ρ,θ, \phi for a particle of mass m subject to a force whose spherical components are F_{\rho},F_{\theta},F_{\phi}. This is just the first part of the problem but the other parts do not seem so bad...

Homework Statement I am having so much trouble with this one problem ( and spherical coordinates in general ). Any help would be amazing: ∫∫∫ 1 / √(x2+y2+z2) Over -4≤x≤4, 0≤y≤√(16-x2), 0≤z≤√(16-x2-y2) Homework Equations The Attempt at a Solution I know that rho2 will...

Homework Statement Set up the triple integral for the volume of the given solid using spherical coordinates: The solid bounded below by the sphere ρ=6cosθ and above by the cone z=sqrt(x2+y2) Homework Equations The Attempt at a Solution I thought i had this set up right where ρ...

Homework Statement f(x,y,z) = 1 x^{2} + y^{2} + z^{2} ≤ 4z z ≥ \sqrt{x^2 + y^2} Homework Equations The Attempt at a Solution How can I know ρ if there is z variable? Do I just square root both 4 and z? For θ, since it is sphere it would be 0 ≤ θ ≤ 2\pi right? for \phi, is...

Homework Statement Using spherical coordinates, find the volume of the solid that lies within the sphere x2+y2+z2=4, above the xy-plane and below the cone z=√(x2+y2)Homework Equations The Attempt at a Solution This is what I have so far...

Homework Statement The question involves a triple integral, but I can figure that out once I know what this looks like visually. It is the graph of ρ = 1 + cos(∅) How exactly would I graph this? Homework Equations x = ρ * sin(∅) * cos(θ) y = \rho * sin(∅) * sin(θ) z = ρ * cos(∅)...

Homework Statement Verify by direct substitution in Laplace's equation that the functions (2.19) are harmonic in in appropriate domains in ℝ2 Homework Equations (2.19)= {u_n(r, \theta)= \lbrace{1,r^{n}cos(n \theta), r^{n}sin(n \theta), n= 1, 2...; log(r), r^{-n}cos(n \theta), r^{-n}sin(n...

I've no idea where to put this question but here it is I am trying to work through the examples our lecture has given in class and I wasn't getting them at all the first thing that confused me was \nabla . \underline{r} = 3 I tried this myself with \nabla . \underline{r} =...

I'm doing a Lagrangian problem in spherical coordinates, and I was unsure how to express the kinetic energy, so I looked it up and wiki states it should be this: http://en.wikipedia.org/wiki/Lagrangian#In_the_spherical_coordinate_system Which would give me the correct answer, but I'm...

I am facing some problem about derivatives in spherical coordinates in spherical coordinates: x=r sinθ cos\phi y=r sinθ sin\phi z=r cosθ and r=\sqrt{x^{2}+y^{2}+z^{2}} θ=tan^{-1}\frac{\sqrt{x^{2}+y{2}}}{z} \phi=tan^{-1}\frac{y}{x} \frac{\partial x}{\partial r}=sinθ cos\phi then \frac{\partial...

So here's the question: An ant crawls on the surface of a ball of radius b in such a manner that the ants motion is given in spherical coordinates by the equations: r = b, \phi = \omegat and \vartheta = \pi / 2 [1 + \frac{1}{4} cos (4\omegat). Find the speed as a function at time t and the...

Homework Statement What is the dot product of two unit vectors in spherical coordinates?Homework Equations A∙B = ||A|| ||B|| cos(\theta) = cos(\theta)The Attempt at a Solution The above equation is the only relevant form of the dot product in terms of the angle \theta that I can find. However...

Hi, I seem to have forgotten some of my math how-to, as I haven't done this in a while. Looking through my notes, Bird, Stewart and Lightfoot, Greenberg, etc. don't really help. My equation is this, at steady state: 0 = 1/r^2 ∂/∂r (D*r^2 ∂C/∂r) + P Where P is some production rate...

I want to study antenna patterns of different arrangements. I am looking for a very cheap software ( free is even better) to plot graph if I provide the \;R,\theta,\phi. Even if 2D plot would be helpful like keeping either \;\theta\;\hbox { or }\; \phi\; constant and vary the other angle to...

I wanted to derive the volume of a sphere using triple integration with spherical coordinates, but instead of taking the limits of θ as (0° ≤ θ ≤ 180°), I chose to take (0° ≤ θ ≤ 360°), and therefore, for φ as (0° ≤ φ < 180°), Now of course the integral of sin(θ) from 0° to 360° is zero, and...

Homework Statement Using spherical coordinates, set up but DO NOT EVALUATE the triple integral of f(x,y,z) = x(x^2+y^2+z^2)^(-3/2) over the ball x^2 + y^2 + z^2 ≤ 16 where 2 ≤ z. Homework Equations x = ρ sin ϕ cos θ y = ρ sin ϕ sin θ z = ρ cos ϕ ρ^2 = x^2 + y^2 + z^2 ∫∫∫w...

Divergence and Curl in cylindrical and spherical co are: \nabla \cdot \vec E \;=\; \frac 1 r \frac {\partial r E_r}{\partial r} + \frac 1 r \frac {\partial E_{\phi}}{\partial \phi} + \frac {\partial E_z}{\partial z} \;=\; \frac 1 {R^2} \frac {\partial R^2 E_R}{\partial R} + \frac 1 {R\;sin...

I want to graph this vector field -^r/r^2 but I don't know how to do. Any help would be appreciated.

Homework Statement Using spherical coordinares, find the smaller volume bounded by the cone z=r and the sphere z^2+y^2+x^2=4 Homework Equations x^2+y^2+z^2=4 ; rho=2, z=rhocosphi The Attempt at a Solution Shot in the dark: Tried function integrating (rho squared - rhocosphi)...

Can anyone show me how you get the curl in polar or spherical coordinates starting from the definitions in cartesian coordianates? I haven't been able to do this.

Hello! My problem is that I want to find (\frac{\partial}{{\partial}x}, \frac{\partial}{{\partial}y}, \frac{\partial}{{\partial}z}) in spherical coordinates. The way I am thinking to do this is...

Homework Statement Calculate the z-component of the centre of mass for a northern hemisphere of radius R with constant density \rho_0 > 0 using spherical coordinates (r,\theta, \varphi ) defined by: x(r,\theta, \varphi) = r\sin\theta\cos\varphi \;\;\;\;\;\;0 \leq r < \infty y(r,\theta...

Homework Statement Find the spherical coordinates of the point with rectangular coordinates (2√2, -2√2, -4√3) Homework Equations ? The Attempt at a Solution The textbook gives the answer as (8, -pi/4, 5pi/6) No idea how to get to this. Any help appreciated.

I'm writing a function for Matlab and I'm trying to figure out how to apply a torque matrix in cartesian coordinates to an object in spherical coordinates. The short story is this: For interest's sake, a friend and I have written a function with creates a tree which random branch...

Homework Statement evaluate the following triple integral in spherical coordinates:: INT(=B) = (x^2+y^2+z^2)^2 dz dy dx where the limits are: z = 0 to z = sqrt(1-x^2-y^2) y = 0 to z = sqrt(1-x^2) x = 0 to x = 1 Homework Equations The only thing I know for sure is how to set...

This is not a homework. Actual this is part of my own exercise on conversion where \vec A = \vec B \;X\; \vec C and I intentionally set up B and C so the \theta_B \hbox { and } \theta_C \;=\; 60^o \; respect to z-axis: \vec B_{(x,y,z)} = (2,4, 2\sqrt{(\frac 5 3)}) \;\;\hbox { and }\;\...

I've got a unit sphere sitting at the origin. This sphere is cut by an arbitrary plane. I'm looking to find the equation of the circle that results from the intersection in spherical coordinates. This is for a computer program I'm writing, and I've already set it up to approximate this by...

Homework Statement This is a bit hard to describe without a decent picture (or a decent brain) but try to bare with me. Picture below shows two spheres, if the origin is at centre of A, and a line d joins the centre of the two spheres, how do I describe the position of a point r from each...

Homework Statement Evaluate by changing to spherical coordinates \int^1_0\int^{\sqrt{1-x^2}}_0\int^{\sqrt{2-x^{2}-y^2}}_{\sqrt{x^{2}+y^2}}xydzdydx Homework Equations dz dy dz = {\rho}^{2}sin{\phi} The Attempt at a Solution This problem is quite simple to do in cylindrical...

Homework Statement Write the vector D_{p}=2\partial/ \partial x-5\partial/ \partial y+3\partial/ \partial z \in T_{p}\Re^{3} in cylindrical and spherical coordinates Homework Equations NA The Attempt at a Solution x=r cost y=r sint z=z ...

Homework Statement Calculate: integral B [ 1/sqrt(x^2+y^2+(z-a)^2) ] dx dy dz , when B is the sphere of radius R around (0,0,0), a>R. Homework Equations The Attempt at a Solution I tried spherical coordinates for the integrand: x=rsin(p)cos(t) y=rsin(p)sin(t) z=rcos(p)+a The problem is when I...

I have a few questions about rotations. First off if i have two vectors r_{a,b}=(1,\theta_{a,b},\phi_{a,b}) And i define \Delta\theta=\theta_b-\theta_a and \Delta\phi=\phi_b-\phi_a. Then take the map T(1,\theta,\phi)=(1,\theta+\Delta\theta,\phi+\Delta\phi). Is T a rotation? I would...

In general, how do I determine the angle phi when you have to use spherical coordinates for integration?

Evaluate the integral by changing to spherical coordinates. Not sure how to go about figuring out the limits of integration when changing to spherical coordinates.

Homework Statement \rho = sin\theta * sin\phi Homework Equations I know that \rho^{2} = x^{2} + y^{2}+z^{2} The Attempt at a Solution I tried converting it to cartesian coordinates but I can't seem to get a workable answer that way. I know that the answer is the sphere with radius...

Hi there. I have some doubts about this exercise. It asks me to use the appropriated coordinates to find the volume of the region indicated below. The region is determined by the first octant under the sphere x^2+ y^2+ z^2=16 and inside the cylinder x^2 +y^2=4x The first thing I did was to...

Homework Statement I have three problems and I could really use some help. 1. Integrate the function f(x,y,z) = y over the part of the elliptic cylinder x^2/4 +y^2/9 = 1 that is contained in the sphere of radius 4 centered at the origin and such that x≥0, y≥ 0, z≥0. 2. Find the total...

Homework Statement use spherical coordinates to calculate the triple integral of f(x,y,z) over the given region. f(x,y,z)= sqrt(x^2+y^2+z^2); x^2+y^2+z^2<=2z The Attempt at a Solution Once I find the bounds, I can do the integral. But I'm having trouble with the bounds of rho. This...

Hello, I am trying to work out how you derive velocity in terms of spherical coordinates, could anyone point me in the direction of a simple and quite explicit derivation. I keep getting confused! Thanks.

I am reading the Wikipedia entry http://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates" . There, in particular I see this: Time derivative of a vector field To find out how the vector field A changes in time we calculate the time derivatives. In cartesian...

I have not done this in a while and I am having a brain fart. Given: A wheel of radius R rotates with angular velocity Ct2 k\hat{} (lies in x-y plane, rotating about z). A point P on the circles is P(x,y,z) = (0,R,0) Ques: What is the position vector of point P in spherical coordinates...

I've been trying to find the exact solution to the advection equation in spherical coordinates given below \frac{\partial{\phi}}{\partial{t}} + \frac{u}{r^2}\frac{\partial{}}{\partial{r}}r^2\phi = 0 Where the velocity u is a constant. First I tried to expand the second term using product...