Lagrange Definition and 542 Threads

Hello there, I am dealing with the functional (http://en.wikipedia.org/wiki/First_variation) J = integral of (y . dy/dx) dx When trying to compute the Euler Lagrange eqaution I notice this reduces to a tautology, i.e. dy/dx - dy/dx = 0 How could I proceed for finding the y(x) that...

Homework Statement Hello. I've been stuck on a Lagrange Multiplier problem. It's from Mathematical Methods in the Physical Sciences by Mary Boas 3rd edition pg. 222. The question is: What proportions will maximize the volume of a projectile in the form of a circular cylinder with one conical...

Hi There I would like help on a question about Lagrange multipliers. Question: Consider the intersection of two surfaces: an elliptic paraboloid z=x^2 + 2*x + 4*y^2 and a right circular cylinder x^2 + y^2 = 1. Use Lagrange multipliers to find the highest and lowest points on the curve of the...

Euler Lagrange Equation : if y(x) is a curve which minimizes/maximizes the functional : F\left[y(x)\right] = \int^{a}_{b} f(x,y(x),y'(x))dx then, the following Euler Lagrange Differential Equation is true. \frac{\partial}{\partial x} - \frac{d}{dx}(\frac{\partial f}{\partial y'})=0...

Homework Statement The center of mass (C) of the circular rolling disc is offset from its centroid (O) by an eccentric distance OC = \epsilon. The radius of the wheel is R. The disc is rolling without slipping at a constant rotational speed \omega by a variable torque T. Solve for this...

I think that many of us have had to endure working with Lagrange multipliers in the past, but it seems to me that it has always been taught incorrectly. So the statement (if you will allow me to use differential forms) is Now my issue is that it's well-known that this should be...

Homework Statement OK I have a Differential Calculus exam next week and I do not understand about Differential Manifolds. We have been given some questions to practise, but I have no idea how to do them, past a certain point. For example 1. Study if the following system defines a manifold...

Homework Statement If L(y, y', x) = y^{2} + y'^{2} then find the appropriate Euler Lagrange Equation. I have absolutely no idea how to solve this. I used the differential form of the Euler Lagrange equations for a stationary action but the answer i got was nothing like the answer in the book...

[PLAIN]http://img337.imageshack.us/img337/3623/pensp.jpg Homework Statement I need to find the equations of motions via Lagrange's formulation when the generalized coordinates are: \vec{q}=[x,y,z]^T2. The attempt at a solution I need to verify whether what I obtained so far is true or not...

So I'm studying for a final, and it just so happens my professor threw taylor polynomials at us in the last week.. I understand the concept of a taylor polynomial but i need some help fully understand the LaGrange remainder theorem if we have a function that has n derivatives on the interval...

Hello physicsforums community. I have recently learned about Lagrange multipliers and have been given three problems to solve. Could you guys please go over my work and see if I have the gist of it? One question, a theoretical one, I have no idea how to begin. Any advice regarding this would be...

Homework Statement im given a matrix A= 1 -2 ///////////////////////-2 4 im told to find the eigen values and the vectors... but the thing is i have never came across this, i learned lagrange multipliers but never used it to find eigen values and vector.. Homework Equations The...

Find the maximum and minimum of f(x,y)=y2-x2 with the constraint x2/4 +y2=2. My calculus professor gave us this on his exam and there were no problems like this in the book and I would just like to know how it's done because it's bothering me ha. After doing the partial derivatives I got...

Homework Statement Find 3 positive numbers x, y and z for which: their sum is 24 and which maximizes the product: P = x2y3z. Find the maximum product. The Attempt at a Solution Ok, I know how to set up the equations. x + y + z = 24 Delta(F) <2xy3z, 2x2y2z, x2y3> fx = 2xy3z...

http://img221.imageshack.us/img221/3754/capturetp.png Just a simple question. I can see that for this to work I need: Trot = 1/5 ma2(thetaDOT + phiDOT)2 Just can't work out what phi has to do with rotational kinetic energy. I would have thought it would need to be simply the same thing but...

Problem: We want to calculate a polynomial of degree N-1 that crosses N known points in the plane. Solution A: solving a NxN system of linear equation (Gauss elimination) Solution B: construction from Lagrange basis polynomials. One of my professors said that the first solution is...

Homework Statement Let G be an abelian group. Suppose p divides ord(G) where p is prime no. Prove G has a subgroup of order p. Homework Equations lagrange theorem converse The Attempt at a Solution i know the converse is lagrange theorem and easy and this is not the case. I know...

Homework Statement Minimise = x2 + y2 subject to C(x,y) = 4x2 + 3y2 = 12. Homework Equations The Attempt at a Solution I let h(x,y) = x2 + y2 + \lambda(4x2 + 3y2 - 12). I got hx = 2x + 8\lambdax = 0, hy = 2y + 6\lambday = 0, but here I get 2 values of \lambda, \lambda = -1/4 &...

I do not have one specific question that needs answering. Rather, it is about Lagrange multipliers in general. So for certain minimization/maximization questions (ie find the shortest distance from some point to some plane) it seems that one could solve the question using lagrange multipliers...

Lagrange Multipliers Question? Homework Statement Find the minimum and maximum values of the function subject to the given constraint. f (x,y,z) = x^2 - y - z, x^2 - y^2 +z = 0 The Attempt at a Solution Okay this is what I did: Gradient f = <2x,-1,-1> Gradient g =...

So, I'm working through some ideas dealing with Lagrange points. I understand that, the rotation and mass of 2 objects in space create stable areas where an object of "insignificant Mass" compared to the objects it's balancing against, allows for the placement of an object in a stable area...

I know full well the proof using Lagrange's thm. But is there a direct way to do this without using the fact that the order of an element divides the order of the group? I was thinking there might be a way to set up an isomorphism directly between G and Z/pZ. Clearly all non-zero elements...

Homework Statement Seems straightforward enough, Lagrangian optimization Homework Equations Find the max of x^-1 + y^-1 subject to the constraint m=x+y The Attempt at a Solution At first I thought no problems, x*=y*=m/2, however: Using the Lagrangian formula yields...

Homework Statement Let G be group, H<G , K<G, if gcd(lHl,lKl)=1, prove that H\bigcapK={1} Homework Equations The Attempt at a Solution so Lagrange theorem says that lHl l lGl, lKl l lGl, and of course 1 is inside both H and K, but how when they are coprime, the element are all...

Homework Statement See figure Homework Equations N/A The Attempt at a Solution Alright we'll this is my first shot at a question like this, so in all honesty I don't know what concepts this question is testing. It mentions finding absolute max/min of a function inside a...

Hi, Dear Math forum users, I was practicing with my optimization course problem and encountered one type of Lagrange multiplier question which I have trouble with. I am wondering if anyone could enlighten me for the following Lagrange problem. function f = x*y*z subject to 4xy+3yz+2xz...

Hi, I'm trying to do a constrained optimization problem. I shall omit the details as I don't think they're important to my issue. Let f:\mathbb R^n \to \mathbb R and c:\mathbb R^n \to \mathbb R^+\cup\{0\} be differentiable functions, where \mathbb R^+ = \left\{ x \in \mathbb R : x> 0...

Homework Statement Using Lagrange multipliers, find the maximum and minimum values of f(x,y)=x^3y with the constraint 3x^4+y^4=1.Homework Equations The Attempt at a Solution Here is my complete solution. I just wanted to make sure there are no errors and I did it correctly. Thanks for any...

I have been reading about Lagrange Multipliers, my book along with wiki and other resources I have read use an intuitive argument on why the max/min contour lines end up tangent to the constraint equation. I don't really understand it, especially considering the obvious flaw as shown by the...

Homework Statement Find the points on the ellipse x2 + 2y2 = 1 where f(x,y) = xy has its extreme values. Homework Equations The Attempt at a Solution f(x,y,z) = x2 + y2 + z2 -- constraint g(x,y,z) = x2 + 2y2 -1 = 0 gradient of f = \lambda * gradient of g 2xi + 2yj + 2zk =...

f(x,y,z)=4x^2+4y^2+z^2 subject to x^2+y^2+z^z=1 So I have: F(x,y,z,c) = 4x^2+4y^2+z^2+L(x^2+y^2+z^2-1) dF/dx = 8x+2xL dF/dy = 8y+2yL dF/dz=2z+2zL Either x=y=0 and L=-1 OR z=0 and L=-4 For first case, z^2=1 therefore z=+/- 1 giving f(0,0,1)=1 For second case, x^2+y^2=1 2x^2=1...

Hello, I am interested in what would happen if a photon became nested inside the Lagrangian point of a binary black hole system that was already far into the process of merging. It seems that the photon would be "frozen."

Homework Statement find the points on the surface x^2-z^2 = 1 which are in minimum distance from (0,0) i should find the points using d = x^2+y^2+z^2 first of all gradf = λ gradg where f = d and g = x^2-z^2 so we have (2x,2y,2z) = λ (2x,0,2z) now 2x = λ2x 2y = 0 => y = 0 2z = λ2z so...

Homework Statement I am doing this lagrange multiplier problem with 2 constraints. I have completely solved it as shown in the image below. I have found that for lambda = 1 and mu = +/- 1/2 I have that x=+/- [sqrt(2)] y=+/- [1/sqrt(2)] and z=+/- [1/sqrt(2)]. So I am trying to figure...

Homework Statement Find the extrema of the given function subject to the given constraint: f(x,y)=x2-2xy+2y2, subject to x2+y2=1Homework Equations Lagrange Multipliers The Attempt at a Solution First, I defined the constraint to be g(x,y)=0, that is, g(x,y)=x2+y2-1 I then set up the usual...

Hey folks. :smile: I have some more or less qualitative questions regarding optimization problems via Lagrange multipliers. I am following the http://en.wikipedia.org/wiki/Lagrange_multipliers" on this one and I am just a little confused by their wording. In the first section titled...

Homework Statement Find the points on the level surface xy2z4=1 that are closest to the origin. Homework Equations Lagrange's method for finding extrema The Attempt at a Solution If I have a level surface F(x,y,z)=c, it's points closest to the origin will be the ones in which...

Find an equation of the largest sphere that passes through the point (-1,1,4) and is such that each of the points (x,y,z) inside the sphere satisfies the condition x^2 + y^2 + z^2 < 136 + 2(x + 2y + 3z) I know this problem requires Lagrange multipliers. I assume that x^2 + y^2 + z^2 is...

Homework Statement Assume that the surface temperature distribution of an ellipsoid shaped object given by 4x2 + y2 + 4z2 = 16 is T(x,y,z) = 8x2 + 4yz - 16z + 600.Homework Equations The Attempt at a Solution I'm assuming we just have to find the maximum value of this function using the lagrange...

I'm trying to figure out how much force, over what period of time, is necessary to reach an earth-moon Lagrange point. L1 is about 323110 kilometers from earth, and an object there could remain (more or less) stationary relative to the Earth and the moon. Earth gravity is working against the...

Homework Statement Why is \nabla f = \lambda \nabla g where f is the function you want to find the extrema of and g is the contraint? Also how would you identify the above in the following Determine the least real number M such that the inequality |ab(a^2-b^2) +...

Homework Statement I'm attempting to solve the following equation: y = xf(y') + g(y') where y' = P y = xf(P) + g(P) Homework Equations I can restate the equation as dx/dP - x f'(P)/(P - f(P)) = g'(P)/(P - f(P)) which is a 1st order differential equation in standard...

Homework Statement y = xf(y') + g(y') Let y' = P taking d/dx and rearranging gives dx/dP - xf'(P)/{P - f(P)} = g'(P)/(P - f(P)) a 1st order linear differential equation in standard form. Homework Equations When I attempt to solve by the suggested standard method, I end up...

Homework Statement A Lagrange differential eq. represented as follows: y = xf(y') + g(y') Let y' = P and after some fancy footwork; dx/dP - xf'(P)/(P - f(P)) = g'(P)/(P - f(P) Homework Equations Now, the link that I got this from states that this is a 1st ode in standard...

Homework Statement Estimate sin4 accurate to five decimal places (using maclaurin series of sin) Homework Equations The Attempt at a Solution Lagrange error bound to estimate sin4° to five decimal places( maclaurin series) 4°=pi/45 radians |Rn(pi/45)<1*(pi/45)^n+1/(n+1)...

Homework Statement Find the optimal value of the function f (x,y) = 3.5x^2+y^2-42x-28y+5xy+190 subject to 6x+5y = 37 Homework Equations Use the second order condition to determine if the optimal point is maximum or minimum The Attempt at a Solution

Homework Statement f(x,y,z)=exy and x5+y5=64 Find Max and MinHomework Equations ∇F = <yexy, xexy> λ∇G = <5x4λ, 5y4λ> The Attempt at a Solution yexy = 5x4λ xexy = 5y4λ x5+y5=64 No idea where to go from here...

Homework Statement if you have dl/dx= -2 +0.002x-lagrange function(backword L) dl/dy=0.012y-5-lagrange function dl/dl= -(x+y-2000) How do you solve for x, y and backword l? Homework Equations The Attempt at a Solution

Hi, I'm trying to implement some equations from a paper. It comes down to a system of 2 coupled ODEs. In one of the ODEs, there are 3 Lagrange multipliers. The paper says that the three multipliers can be determined by three integral constraints (integrals of some functions of the...

Homework Statement Use lagrange multipliers to find the shortest distance between a point on the elliptic paraboloid z=x^2 +y^2 Homework Equations The Attempt at a Solution http://img716.imageshack.us/img716/7272/cci1902201000000.jpg I'm not that good with using the equation...