Ellipsoid Definition and 99 Threads

This isn't homework or anything, I just want to understand the question better. Homework Statement The Attempt at a Solution I'm honestly not sure where to go with this. Is this an integral problem? As I understand it I'm finding the area of a slice, not a volume of the whole...

Homework Statement Consider the ellipsoid L \subsetE3 specified by (x/a)^2 + (y/b)^2 + (z/c)^2=1 (a, b, c \neq 0). Define f: L-S^{2} by f(x, y, z) = (x/a, y/b. z/c). (a) Verify that f is invertible (by finding its inverse). (b) Use the map f, together with a smooth atlas of S^{2}, to...

I have a matrix D (it happens to be in R^(nxm) where n>>m, but I don't think that is relevant at this point). I also have a vector t in R^n. I am interested in rewriting the set {x | (Dx-t)'(Dx-t) <= c} in standard ellipsoid form: --> {x | (x-z)'E(x-z)<=b} where E is an mxm positive...

In this context, the support mapping of any convex geometry is any point on the geometry which results in the largest dot product to some direction vector. I would appreciate some help in computationally finding the support mapping of an arbitrary ellipsoid (some arbitrary orthonormal basis...

Right now I'm running this with a brute force program which takes points on an ellipsoid and checks the distance to the point, slightly readjusts, and keeps moving toward the minimum, but it takes far to long for the mass amount of points I want to run through the program. Is there an equation I...

Homework Statement How to calculate the radiation from i) vibrating ii) rotating ellipsoid? Homework Equations The Attempt at a Solution Rotating ellipsoid has a time dependant dipole moment so the radiation pattern will be of electric dipole type (The magnetic dipole and...

I have an important paper to submit and I have a feeling I didn't solve the following correctly. I have to find the maximal volume of a Cuboid inscribed inside half of the Ellipsoid D={(x,y,z): x^2/a^2 + y^2/b^2 + z^2/c^2 <=1, z>=0 } So I decided to use Lagrange's multipliers. That's...

Homework Statement Problem 2 b) in the following link http://www.math.ubc.ca/~haber/courses/math253/Welcome_files/asgn4.pdf" Homework Equations V=pi(r1r2)H SA=? The Attempt at a Solution I was thinking I should form two equations V=10=pi(r1r2)h and then an equation for the...

I wanted to get opinions on whether solving this problem in a non-numerical way is realistic, or if someone has the answer, all the better. I have a totally arbitrary ellipsoid (not aligned with any axes) that I can describe by matrix A, like x'Ax=1 is the ellipsoid surface. I have the points...

Asuming a uniform distribution, how can I find the center of mass of a planet such as Earth?

Homework Statement The problem asks to find the shortest distance between two points on Earth, assuming different equatorial and polar radii i.e. the coordinates are represented as: x = a*cos(theta)*sin(phi) y = a*sin(theta)*sin(phi) z = b*cos(phi) Homework Equations The Attempt at a...

Homework Statement Find the surface area of that part of the plane 9x+10y+z=6 that lies inside the elliptic cylinder \frac{x^2}{25} +\frac{y^2}{100} =1 2. The attempt at a solution Once again I was just told that the surface area would be equal to the double integral of the area...

I seem to be off by a factor of 2 on the answer to this problem but I can't find where I went wrong. The term in front should be 1/5 and not 2/5. Does anybody see the mistake in my work? It is attached in a word document because I can't figure out how to put the equations into this post...

Hello mathematicians, I'm a physics masters student and working on a subject where I have to create some random polyhedra for some purpose. I devised an algorithm to create polyhedra by assigning points on the surface of an ellipsoid, but someone told me that this causes a tough restriction...

I have been asking/looking around for the general equation of an ellipsoid and I am unable to find it anywhere. Does anyone know what it is? BTW: What I mean by the general equation of an ellipsoid, one that can be rotated in any way, that is 2 angles of rotation and one that does not...

Ok so basically what I'm trying to model is an ellipsoid on a plane, the planes angle can be changed by the user and the ellisoid should move accordingly. But I have absolutely no idea where to start. I've tried finding equations etc but I could't find anything other than the equation of an...

Homework Statement I have two surfaces, a cylinder and an ellipsoid. I want to find the volume bounded by those two surfaces. The sufaces are: S x^{2}+y^{2}=4 and M 4x^{2}+4y^{2}+z^{2}=64Homework Equations reparameterize it to get it in the form: \int\int_{D}(S-M)dA If you do this and...

I know this has been answered in another thread, but it still isn't entirely clear to me. This particular section in class is giving me some major problems and I'm hoping someone can shed some light on things. This is probably one of the easier problems in this assignment and I'm hoping if I...

Hi, I'm a biology PhD student looking for some help on how to calculate (or estimate) the surface area of an ellipsoid truncated parallel to the long axis. Any help would be greatly appreciated. Thanks, Murphy24

Problem: Find the principal moments of inertia of an ellipsoid. I began to label moments of intertia about minor axises. But I'm not sure where to go after that.

Hi, everybody. Is this tank an ellipsoid? If not, what shape is it?

Hi, given an ellipsoid in parametric form in t, I was trying to get to the classical equation in x,y. Things are very straightforward, as long as the ellipse radii are aligned with the principal axes. Instead, I am trying to find the equation of a "rotated" ellipse, given a parametrization in...

Homework Statement An ellipse is rotated around the y-axis, find the volume of this solid. Homework Equations x^2 / a^2 + y^2 / b^2 = 1 \pi\int_{a}^-a x^2 dy The Attempt at a Solution I'm having trouble solving this; I know that the upper and lower bounds of the curve occur on...

Homework Statement Describe and sketch the surface. (y^2)+(4z^2)=4 Homework Equations It appears that the sketch will be an ellipsoid. Because the problem instructs me to describe and sketch the surface, I don't believe there are any useful equations. The Attempt at a...

discuss how to find the umbilic points of an ellipsoid and their connection to lines of curvature.

who can help me with this: on an ellipsoid most points are not umbilic, but there are some special places that are. Discuss how to find these points and their connection to lines of curvature.

Homework Statement I have an ellipsoid with center (000). There is a point A inside the ellipsoid with known coordinates(1,2,3) I draw a line from center to point A and extend it to cut the ellipsoid on on point p(x,y,z). 2. Homework Equations I want to find the coordinates of...

I have a point p(xp,yp,zp) inside an ellipsoid and i want to find the angle of that point from the center of the ellipsoid(xc,yc,zc) . I also have the major axis length 'a' ,with length ax,ay and az components I calculated the unit vector of axis a with formula length of axis...

Homework Statement I have a point p(xp,yp,zp) inside an ellipsoid and i want to find the angle of that point from the center of the ellipsoid(xc,yc,zc) . I also have the major axis length 'a' ,with length ax,ay and az components I calculated the unit vector of axis a with formula...

Homework Statement Let r(x,y,z)=<x,y,z>. Compute the outward flux of F=r/|r|^3 through the ellipsoid 4x^2+9y^2+6z^2=36. Homework Equations The Attempt at a Solution I know that I can't use the divergence theorem on the region inside S because F isn't continuous at 0. But I can do...

Hi. When reducing the value of measured gravity to produce gravity anomalies, the measured gravity is reduced to it's value on the geoid (conventional interpretation). This is then compared to the value generated by the reference ellipsoid at the ellipsoid surface. I would have thought...

The one formula I need I cannot find. I have an Oblate Ellipsoid which I can describe as a=b=2c. The values of a, b, and c are known to me. I've encountered multiple representations of symbols here, so... let Phi = angle from positive z-axis: 0<= Phi <=180. let Theta = angle from...

A little background first is that I'm currently a rising Sophomore at Winthrop University in South Carolina. I am a Computer Science and Mathematics Double Major. After finishing half-way through third semester calculus and dealing with 3-Dimensional space, vectors, planes, and surfaces, I...

Challenging Problems Develop a formula for the volume of an ellipsoid of the form x2\a2 +y2\b2 +z2\c2 = 1 pls Help me; I need the answer today

I am looking for a term to describe the widest part of an ellipsoid. However this ellipsoid is irregularly shaped because it's a wine glass. As the glass goes up from the stem it continues to widen and then toward the brim it begins to narrow again just a little. So basically it is an ellipsoid...

So I have an array p(t) = e + td, where e is the start position, t is some parameter, and d is the direction of the ray For a sphere with center c and radius R, the vector form equation is (p-c).(p-c)-R^2=0 This can be algebraically manipulated into: t = (-d.(e-c) +- sqrt((d.(e-c))^2 -...

Homework Statement Particles of scattered off the surface of an ellipsoid given by x^+y^2+z^2/f^2 = R^2, where f and R are constants. Find the differential cross-section.Homework Equations The Attempt at a Solution Let s be the impact parameter. I can find s as a function of the scattering...

Homework Statement Find an equation for the plane consisting of all points that are equidistant from the points (1,0,-2) and (3,4,0) Homework Equations The Attempt at a Solution I found the midpoint ant (4, 4, -2), which I believe is the center. However, I have no idea on how...

Is anyone familiar with the concept of a probability tensor or a probability ellipsoid? I am learning about them in the context of NMR techniques. Here is a page describing them: http://www3.interscience.wiley.com/cgi-bin/abstract/107633228/ABSTRACT?CRETRY=1&SRETRY=0 My question is, why...

Homework Statement A uniform symmetric ellipsoid (Mass M) has a large semi axis c and small semi axis a. A particle of mass m<<M is moving along a straight line parallel to the x-axis with speed v(i). Its y-coordinate is a/2 and its z-coordinate it c/2. After an inelastic collision, it sticks...

I'm trying to find the largest sphere that be inscribed inside the ellipsoid with equation 3x^2 + 2y^2 + z^2 = 6. Homework Equations I know I will need at least 2 equations. One of them is the constraining equation (f(x) = a, where 'a' is a constant) and the other is the equation you...

We have an ellipsoid with the equation 4x^2 + y^2+ 4z^2 = 16, and it is raining. Gravity will make the raindrops slide down the dome as rapidly as possible. I have to describe the curves whose paths the raindrops follow. This is probably more vector calculus than physics, but i wasn't sure...

Hello! I am trying to find the normal to an ellipsoid of the form x^2/a^2 + y^2/b^2 + z^2 = 1 What I did is the following: Let psi = x^2/a^2 + y^2/b^2 + z^2 then grad psi (and thus the normal) is: grad (psi) = (2x/a^2, 2y/b^2, 2z) = n Could anyone tell me whether that...

Well, I have a small problem. I know the general formula for the volume of an ellipsoid. But I have a task to find it with the help of an integral. Can you explain me how to do this?

I've been asked to derive an expression for the volume of an ellipsoid. I know what the expression is, I just don't know how to get there from the information given. All that is given is that it is defined by \frac{x^2}{a^2} +\frac{y^2}{b^2} +\frac{z^2}{c^2} \leq 1, a standard...

Find the volume of the ellipsoid x^2 + y^2 + 10z^2 = 16 solve for z... z=sqrt((16-x^2-y^2)/(10)) z = sqrt((16-r^2)/10) so to find the volume, my integral looks like this: latex doesn't seem to be working, so this could look messy... 2*int (from 0-2pi)*int(from 0-1)*...

I need help with two questions. Find a divergent improper integral whose value is neither infinity nor -infinity. 2. Find the volume of an ellipsoid (a^2*x^2) + (b^2*8y^2) + (c^2*z^2) = a^2*b^2*c^2 using integration.

What is the general equation for an ellipsoid (i.e., the general equation of a sphere is (x-h)^2 + (y-j)^2 + (z-k)^2 = r^2 Where (h, j, k) is the center of the sphere) ?

"Hi, I have a question on max vol. q. Its invloved with multivariable calculus. Q) Find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 9x^2+36y^2 + 4z^2 = 36. What i did was i found the three x,y and z-intersection points...