Lagrange Definition and 510 Threads

When I try to solve a linear program using matlab,after using linprog(f,A,b,...) I can find the Lagrange multiplier associated with the inequality constraints and the lower bound constraints by using: lambda.ineqlin ; lambda.lower But if I want to solve a quadratic program (using...

Homework Statement The lagrange equations are obtained as in the picture. I am only showing the final part of the solution, where they consider the final case of x≠y≠z. Homework Equations The equation at the second paragraph is obtained by subtracting: (5.34 - 5.35). The final equations are...

Homework Statement This section describes the "Lagrange undetermined multipliers" method to find a maxima/minima point, which i have several problems at the end. The Attempt at a Solution Why are they adding the respective contributions d(f + λg), instead of equating df = λdg ? Imagine...

Hello everyone! I just finishexd reading Death By Black Hole and I was interested in the Lagrange points. Neil talks about how if you placed objects inside of them you could use the points as place holders for objects while building in space. I couldn't seem to find anything about the width of...

Homework Statement I need to find the extrema of f(x,y) = 3x^{2} + y^{2} given the constraint x^{2} + y^{2} = 1 Homework Equations I'm not sure what goes here. I've been trying to solve it with this: ∇f(x,y) = λ∇g(x,y) The Attempt at a Solution f(x,y) = 3x^{2} + y^{2} g(x,y)...

Hello all, I am having some frustration understanding one derivation of the Euler Lagrange Equation. I think it most efficient if I provide a link to the derivation I am following (in wikipedia) and then highlight the portion that is giving me trouble. The link is here If you scroll...

Homework Statement Show that , the maximum value of function f(x,y) = x^2 + y^2 is 70 and minimum value is 20 in constraint below. Homework Equations Constraint : 3x^2 + 4xy + 6y^2 = 140 The Attempt at a Solution Book's solution simply states the Lagrange rule as ...

Homework Statement What I don't understand is why you can maximize the distances squared - d2. Isn't d2 different from d? I don't see how they can get you the same value.

Homework Statement My question refers to the paper "Topological Sigma Models" by Edward Witten, which is available on the web after a quick google search. I am not allowed to include links in my posts, yet. I want to know how to get from equation (2.14) to (2.15). We consider a theory of maps...

Consider $${f (x, y) = x^2 + 2 y^2}$$ subject to the constraint $${x^2 + y^2 = 1}$$. What would be the minimun and the maximum values of the f. Trouble is when I tried solving the problem lamda comes out to have two values 1 and 2 respectively. How do I proceed in order to get the answers?

Lagrange & Euler formalism How we get relation (\frac{\partial T^{(L)}}{\partial t})_{r_0}=(\frac{\partial T^{(E)}}{\partial t})_{r}+\frac{\partial T^{(E)}}{\partial x}(\frac{\partial x}{\partial t})_{r_0}+\frac{\partial T^{(E)}}{\partial y}(\frac{\partial y}{\partial...

Homework Statement The problem of minimizing f(x1, x2) = x1^3 subject to (x1 + 1)^3 = (x2 − 2)^2 is known to have a unique global solution. Use the method of Lagrange multipliers to find it. You should deal with the issue of whether a constraint qualification holds. Homework Equations...

I want to prove that Euler Lagrange equation and Einstein Field equation (and Geodesic equation) are the same thing so I made this calculation. First, I modified Energy-momentum Tensor (talking about 2 dimension; space+time) : T_{\mu\nu}=\begin{pmatrix} \nabla E& \dot{E}\\ \nabla p &...

Proof using lagrange! Homework Statement (A x B) . (C x D) = (A . B) (C . D) - (A . D) (B . C) Homework Equations This is all that's given..I am sort of lost on how to proof this. Spent 4hrs + The Attempt at a Solution Completely lost and don't know where to start

Guys, i would be really greatfull if someone help me with this because i really don't know how to deal with this math problem: Find the maximum and minimum values of f = x^(1/4) + y^(1/3) on the boundary of g = 4*x+ 6*y = 720. Please help me someone, i am desperate from this :(

Does anyone have any tips for solving the system of equations formed while trying to find Lagrange Multipliers? I have searched for videos online (patrickjmt and the MIT lecture on Lagrange Multipliers) but I still find it a bit confusing.

Homework Statement Find the stationary value of $$ f(u,v,w) = \left( \frac{c}{u} \right)^m + \left( \frac{d}{v} \right)^m + \left( \frac{e}{w} \right)^m $$ Constraint: $$ u^2 + v^2 + w^2 = t^2 $$ Note: $$ u, v, w > 0 $$. $$ c,d, e, t > 0 $$. $$ m > 0 $$ and is a positive integer.Homework...

Homework Statement An open gutter with cross section in the form of a trapezoid with equal base angles is to be made by bending up equal strips along both sides of a long piece of metal 12 inches wide. Find the base angles and the length of the sides for maximum carrying capacity. For more...

Homework Statement (a) If x_{1},\ldots, x_{n} are distinct numbers, find a polynomial function f_{i} of degree n - 1 which is 1 at x_{i} and 0 at x_{j} for j \ne i. Hint: the product of all (x - x_{j}) for j \ne i is 0 at x_{j} if j \ne i. This product is usually denoted by \prod_{\substack{j...

Homework Statement Find the product of the maximal and the minimal values of the function z = x - 2y + 2xy in the region (x -1)2+(y + 1/2)2≤2 Homework Equations The Attempt at a Solution I have taken the partial derivatives and set-up the problem, but I am having difficulty...

Lagrange Multiplier --> Find the maximum. Homework Statement Find the maximum value, M, of the function f(x,y) = x^4 y^9 (7 - x - y)^4 on the region x >= 0, y >= 0, x + y <= 7. Homework Equations Lagrange multiplier method and the associated equations. The Attempt at a Solution...

Homework Statement Find the maximum and minimum values of f(x,y) = 2x^2+4y^2 - 4xy -4x on the circle defined by x^2+y^2 = 16. Homework Equations Lagrange's method, where f_x = lambda*g_x, f_y= lambda*g_y (where f is the given function and g(x,y) is the circle on which we are looking...

Homework Statement Attached as Question.jpg. Homework Equations Partial differentiation. Lagrange multiplier equation. The Attempt at a Solution Attached as MyWork.jpg. Is my work correct? I'm still not confident with myself for these problems and it would be great if someone...

For functional J(q_1,...,q_n)=\int^{t}_{t_0}L(q_1,...,q_n;\dot{q}_1,...,\dot{q}_n;t) Why isn't J(q_1,...,q_n;\dot{q}_1,...,\dot{q}_n;t)?

Homework Statement f(x,y) = y2-x2, g(x,y) = x2/4 +y2=9 Homework Equations \nabla f = \lambda \nabla g -2x = \lambda \frac{x}{2} 2y = 2\lambda y \frac{1}{4} x^2 + y^2 = 9 The Attempt at a Solution I arrived at the three equations above. So according to the first equation...

Homework Statement When a rectangular box is sent through the mail, the post office demands that the length of the box plus twice the sum of its height and width be no more than 250 centimeters. Find the dimensions of the box satisfying this requirement that encloses the largest possible...

Homework Statement Not really a homework question, just want to check out if what I'm doing is right. I challenged myself to find the equation of motion and the forces in the simple pendulum system but with using the Lagrange multipliers and the constraint equation.Homework Equations In next...

Hi all, first post, please bear with me! I am trying to understand Lagrange's Theorem by working through some exercises relating to the Orbit-Stabilizer Theorem (which I also do not fully understand.) I think essentially I'm needing to learn how to show cosets are equivalent to other things or...

Homework Statement I am having trouble understanding how to apply Lagrange's equation. I will present a simplified version of one of my homework problems. Imagine an inverted pendulum, consisting of a bar attached at a hinge at point A. At point A is a torsional spring with spring...

Homework Statement The question is : Find the maximum and minimum lengths of the radius vector contained in an ellipse 5x^2 +6xy+5y^2 Homework Equations The Attempt at a Solution Hi I seem to be at a loss here because usually along with an equation a constraint is also given but in this case...

Homework Statement Hello! I'm having some difficulty getting the objective function out of this question, any help/hints would be appreciated >.< Company A prepares to launch a new brand of tablet computers. Their strategy is to release the first batch with the initial price of p_1 dollars...

Homework Statement Prove that (A x B) . (u x v) = (a.u) (b.v) - (a.v)(b.u) The Attempt at a Solution I've used lagrange indentity to proof that. but I can't go ahead Thanks

Maximize: 3*v*m subject to: L - m - v >= 0 V - v >= 0 m - 6 >= 0 M - m >= 0 Where L, M, and V are positive integers. Lagrangian (call it U): U = 3vm + K1(L - m - v) + K2(V - v) + K3(m - 6) + K4(M - m) Where K1-K4 are the slack variables/inequality Lagrange...

The problem: Minimize tr{RyxR} subject to RTR=I This problem is known as Procruses Analysis and can be solved using Lagrange Multipliers, so there's a tendency to write the following function: L(R) = tr{RyxR} - \Lambda(RTR-I), where \Lambda is a matrix of Lagrange Multipliers However, there...

Homework Statement A particle of mass m is connected by a massless spring of force constant k and unstressed length r0 to a point P that is moving along a horizontal circular path of radius a at a uniform angular velocity ω. Verify the Lagrange-Function! Homework Equations Could...

I encountered this beautiful theorem and then I tried hard to prove it using ordinary algebraic methods and my understanding of calculus without involving real analysis in it but I didn't succeed. The theorem states that if f is an analytical function at some point x=a then f-1 has the following...

Homework Statement A cannonball is heated with with temperature distribution T(x,y,z)=60(y2+z2-x2). The cannonball is a sphere of 1 ft with it's center at the origin a) Where are the max and min temperatures in the cannonball, and where do they occur?Homework Equations \nablaf=λ\nablag Where...

Hello there, I am interested in the following matter. Given an ODE, can one always find a functional F such that the ODE is its Euler Lagrange equation? I am thinking at the following concrete case. I have the ODE y' = a y I would like a functional given by the intergral over a...

Homework Statement I'm given that the function f(x) is n times differentiable over an interval I and that there exists a polynomial Q(x) of degree less than or equal to n s.t. \left|f(x) - Q(x)\right| \leq K\left|x - a\right|^{n+1} for a constant K and for a \in I I am to show that Q(x)...

Homework Statement Prove I=T1+T2+...+Tk Where Ti=pi(T) Homework Equations T is kxk pi(x)=(x-c1)...(x-ck) is the minimal polynomial of T. pi=\pii(x)/\pii(ci) \pii=\pi(x)/(x-ci) To evaluate these functions at a matrix, simply let ci=ciI The Attempt at a Solution From lagrange interpolation...

My question is simple is every classical mechanics problem which is solvable by Lagrangian & Hamiltonian methods also solvable by Newtonian methods of forces and torques? And why does it seem that LH make solutions to be a lot more easier than Newtonian methods, and is it always this way?

In Lagrangian mechanics, can anyone show how to find the extrema of he action functional if you have more constraints than degrees of freedom (for example if the constraints are nonholonomic) using Lagrange Multipliers? I've looked everywhere for this (books, papers, websites etc.) but none...

Homework Statement Find the minimum and maximum values of the function subject to the given constraint f(x,y) = x^2 + y^2, 2x + 3y = 6 Homework Equations \nablaf, \nablag The Attempt at a Solution After doing all the calculation, x value and y value came out to be...

Hi Homework Statement Look at the drawing. Furthermore I have a constant acceleration \vec g = -g \hat y I shall find the Lagrange function and find the equation of motion afterwards.Homework Equations Lagrange/ Euler function and eqauation The Attempt at a Solution I found out the...

Homework Statement Find the maximum and minimum values of f(x,y) = x5y3 on the circle defined by x2 + y2 = 10. Do the same for the disc x2 + y2 ≤ 10. The Attempt at a Solution for the first part, if I call the circle g(x,y) defined by x2 + y2 = 10 I need to now define some F(x,y,λ) =...

Hello Can any1 recommend a book that will show the derivation of the Euler-Lagrange equation. (I am learning in the context of cosmology ie. to extremise the interval). Ideally the derivation would be as simple/fundamental as possible - my maths is not up to scratch!

Homework Statement "Vary the following actions and write down the Euler-Lagrange equations of motion." Homework Equations S =\int dt q The Attempt at a Solution Someone said there is a weird trick required to solve this but he couldn't remember. If you just vary normally you get \delta...

Homework Statement Use the method of Lagrange multipliers to find the maximum and minimum values of the function f(x, y) = x + y2 subject to the constraint g(x,y) = 2x2 + y2 - 1 Homework Equations none The Attempt at a Solution We need to find \nablaf = λ\nablag Hence...

Hello everyone, i have 2 problems in my multivariable calculus homework that i can't solve . Please help me out, thank you so much 1/f(x,y)= [(x^2) -2y]^(0.5) a) Find directional derivatives of f at (2,-6) in the direction of <-4,3> b) Find equation of the tangent plane to the function...

Homework Statement Use Lagrange multipliers to find the max and min values of the function subject to the given constraints: f(x1,x2,...,xn) = x1 + x2 + ... + xn constraint: (x1)^2 + (x2)^2 + ... (xn)^2 = 1 The Attempt at a Solution fo x1 to xn values, x must equal 1/sqrt(n) in...