Lagrange Definition and 542 Threads

Homework Statement Find the max and min values of f(x,y,z) = x3 - y3 + 6z2 on the sphere x2 + y2 + z2 = 25. Homework Equations I will use λ to denote my Lagrange multipliers. The Attempt at a Solution So clearly there is no interior to examine since we are on the boundary of the sphere...

Consider a rectilinear rod (A-B) with negligible mass that is attached, without friction, to a vertical OZ axis. The rod rotates about that axis with a constant angular velocity ω and it maintains a angle α with OZ. A particle of mass m moves about the rod and it is attracted by the...

Hi, I have problem with the calculation the error caused by the lagrange inversion. Hence, accroding to Lagrange theorem if f(w)=z it is possible to find w=g(z) where g(z) is given by a series. I wonder, if I consider up to N-th term in the Lagrange series, what will be the error caused by...

Homework Statement Find the maximum and minimum values of 2x2 + y2 on the curve x2 + y2 - 4x = 5 by the method of Lagrange Multipliers. Homework Equations I will express my Lagrange multipliers as λ. The Attempt at a Solution Okay so we want the max min of f(x,y) = 2x2 + y2 given...

Homework Statement If n is a fixed positive integer, compute the max and min values of the function (x-y)^n = f(x,y), under the constraint x^2 + 3y^2 = 1 The Attempt at a Solution I got the 4 critical points (±\frac{\sqrt{3}}{2}, ±\frac{1}{2\sqrt{3}})\,\,\text{and}\,\...

I understand that for Lagrange multipliers, ∇f = λ∇g And that you can use this to solve for extreme values. I have a set of questions because I don't understand these on a basic level. 1. How do you determine whether it is a max, min, or saddle point, especially when you only get one...

Homework Statement Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y) = exy; g(x,y) = x3 + y3 = 16 Homework Equations ∇f(x,y) = λ∇g(x,y) fx = λgx fy = λgy The Attempt at a Solution ∇f(x,y) = < yexy, xexy > ∇g(x,y) = <...

In Goldstein, the action is defined by I=\int L dt. However, when dealing with constraints that haven't been implicitly accounted for by the generalized coordinates, the action integral is redefined to I = \int \left( L + \sum\limits_{\alpha=1}^m \lambda_{\alpha} f_a \right) dt. f is...

Homework Statement A particle of mass m is placed on top of a vertical hoop of radius R and mass M. The particle is free slide on the outside of the hoop without friction while the hoop is free to roll in a vertical place without slipping. Use the method of Lagrange multipliers to determine...

Normally lagrange multipliers are used in the following sense. Suppose we are given a function f(x,y.z..,) and the constraint g(x,y,z,...,) = c Define a lagrange function: L = f - λ(g-c) And find the partial derivatives with respect to all variables and λ. This gives you the extrema...

I have been reading a little about calculus of variations. I understand the basic method and it's proof. I also understand Lagrange multipliers with regular functions, ie since you are moving orthogonal to one gradient due to the constraint, unless you are also moving orthogonal to the other...

Linearization of Lagrange EOMs of an Inverted Pendulum Hi Folks, I am modelling a state space model of an Inverted Pendulum mounted on a cart over a balancing seesaw. I developed the equations of motion using the Lagrangian approach an obtained 3 PDEs. I solved them using Mathematica 8...

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 I'm having trouble grasping http://www.math.tamu.edu/~vargo/courses/251/HW6.pdf. Our teacher has decided to combine elements from Linear Algebra, and understanding Quadratic forms with our section on lagrange multipliers. I am barely able to follow his lectures. If I look...

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...

My instructor likes to explain his topics at light speed and I could barely understand how to use Calculus of variations and the La Grange equations to solve this so I need some help please. This is the problem: Consider the functional for W = w(x,y) prescribed on partial(D), I(W) =...

I have the analytical first and second derivatives of a (multidimensional) lagrangian ( l = f - λh). X is the vector of variables of the objective function and λ is the single lagrange multiplier. where f=f(X) is the nonlinear objective function, h is the nonlinear (equality) constraint (i.e...

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...