Lagrange Definition and 510 Threads

Homework Statement The Park Service is building shelters for hikers along the Appalachian Trail. Each shelter has a back, a top, and two sides. Find the dimensions that will maximize the volume while using 384 square feet of wood. They want me to find the length, width, and height...

I'm having a little trouble with another old test question. It states: Use LaGrange multipliers to find the point on the line 2x + 3y = 3 that is closest to the point P(4, 2). I assume that my constraint is g(x, y) = 2x + 3y = 3, and I have to come up with a function f(x, y) to be...

Hi Everyone, I want to use the Lagrange approach (which I am not terribly familiar with) to model a system with friction. I was thinking of modeling the losses due to friction as a simple constant dissipation of energy over time. Can I simply add a term of the form -Ft to the potential...

Homework Statement A uniform hoop of mass m and radius r rolls without slipping on a fixed cylinder of radius R. The only external force is that of gravity. If the smaller cylinder starts rolling from rest on top of the bigger cylinder , use the method of lagrange multipliers to find the point...

Homework Statement A particle moves on the surface of a sphere. Write down the Lagrange equations.Homework Equations The Attempt at a Solution So since it is a free particle, there is no V in the Lagrangian, correct? So L = T and I can write: L = 1/2 m (R^2 \cos^2 \phi \dot{ \theta}^2 + R^2...

Lagrange equation of motion (from Marion 7-7) A double pendulum consists of two simpe pendula, with one pendulum suspended from the bob of the other. If the two pendula have equal lenghts and have bobs of equal mass and if both pendula are confirned to move in the same plane, find...

Hi! I've been studying Dirac's programme for some time and I realized that there's something missing: Actually this is missing in every standard book on classical mechanics concerning how constraints are implemented in the lagrangian. They are usually inserted with some unknown variables...

hi, i just learned about lagrange multipliers and i am very confused about how to derive and use them. another thing, how would you use them to find points on a surface that are closest to a given point outside the surface

Homework Statement find the max and min of f(x,y)=x^2y, constraint x^2+y^2=1 Homework Equations None. The Attempt at a Solution I found that possible points use the procedure of the method of lagrange multiplier, I got (\pm\sqrt{2/3}, \pm\sqrt{1/3} so 4 points total. But do I have to...

Homework Statement Find the maximum x1, x2, x3, in the ellipsoid x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1 and all the places where this value is attained.Homework Equations The Attempt at a Solution My teacher said to use the lagrange multiplier. So far, I have that we are maximizing x1, x2, and x3...

There's a homework problem that I've been struggling over: Find a formula for the truncation error if we use 1 + x^2 + x^4 +x^6 to approximate 1/(1-x^2) over the interval (-1, 1). Now, I assume that you need to use LaGrange error but I'm not sure how to proceed. Any help would be greatly...

Question: Use Lagrange multiplier method to determine the point on the curve y=1-x^2 that maximises the function f(x,y)=2x + y. Hence find the maximum value of f. Attempt at Solution: Okay I used the Lagrange method to get a point on the curve and I got (1,0) How do I find the...

Consider the function f(t) = ln (1 +2x) Give a formula for f^(n) (x) [**the nth derivative] valid for all n >= 1 and find an upper bound for | f^(n) (x) | on the interval -0.25 <= x <= 0.25. [ the error ]. I found the nth derivative to be f^(n) (x) = (-1)^n+1 * 2^n /n * n...

When we seek the extreaml value of the functional \Phi(\gamma) = \int_{t_0}^{t_1} L(x(t),\dot{x}(t),t)dt where x can be taken from the entire E^n then we come to the well-known Lagrange equations. Now when we are given a constraint, that x \in M, where M is a differentiable manifold and when...

I've just started multi dimensional calculus, among which Langrange's Multipliers. I have some questions which will help me grasp the concepts since I'm a very curious guy... a) What are you finding exactly with this technique? b) What is the constraint? c) What does the extra variable...

My math is a little rusty and I want someone to identify the category of problem (Lagrange Multipliers, Simplex method, ...) I have, so that I can read up on the topic and familiarize myself with the technique. To make the problem simple, let's say I have some number of chips of varying...

Hey, I need help with a problem involving Lagrange multipliers... Here is the question: Find the absolute maximum and minimum of the function f(x,y) = x^2-y^2 subject to the constraint x^2+y^2=289. As usual, ignore unneeded answer blanks, and list points in lexicographic order. I...

Hi, how do I interpret the last sum: http://planetmath.org/encyclopedia/LagrangesIdentity.html Sum (...) 1<=k < j <= n Is it the double sum: Sum( Sum( (a_k*b_j - a_j*b_k)^2 from k = 1 to n) from j = 2 to n ) ?

Hello everyone Here is my problem lagrange interpolation polynomial across the points([SIZE="5"]x0,[SIZE="5"]y0),([SIZE="5"]x1,[SIZE="5"]y1) and ([SIZE="5"]x2,[SIZE="5"]y2) is given by [SIZE="5"]y[SIZE="1"]0[SIZE="5"]L[SIZE="1"]0([SIZE="5"]x) +...

How does one go about computing the locations of the 5 largrange points? I know where they are but do not know how to derive the equilibrium equations. I know you will get a quintic polynomial which can be solved numerically depending on the masses of the two large bodies, but using forces, how...

In my comp physics class, we've been introduced to both c++ and fortran languages. For instance, for our first assignment, I am not sure how to go about investigating the quality of interpolation points for i.e f(x)=sin(x^2) by using n-point langrange interpolation, where n is an input...

Show that if we have N positive numbers \left[ p_{i}\right]_{i=1}^{N} such that \sum_{i} p_{i} =1 then for any N numbers \left\{x_{i}\right\}_{i=1}^{N} we have the inequality \prod_{i=1}^{N} x_{i}^{2 p_{i}} \leq \sum_{i=1}^{N} p_{i}x_{i}^{2} So I am thinking...

Hi, I'm stuck on the following questions and would like some help. 1. A percel delivery service requires that the dimension of a rectangular box be such that the length plus twice the width plus twice the height be no more than 108 centimetres. What is the volume of the largest box that the...

Hey a friend asked me for help on his physics homework, and I found this place and was wondering if you guys could help me out. 2: In 1772, the famed Italian-French mathematician Joseph Louis Lagrange was working on the infamous three-body problem when he discovered an intersting quirk in the...

1: Determine the escape speed of a rocket on the far side of Ganymede, the largest of Jupiter's moons. The radius of Ganymede is 2.64 X 10^6m, and its mass is 1.495 X 10^23 kg. The mass of Jupiter is 1.90 x 10^27 kg, and the distance between Jupiter and Ganymede is 1.071 X 10^9m. Be sure to...

A long first post, but not too hard! dont worry about this i already solved it thanks anyway! The lagrangian of a particle of mass m moving under constant gravity is \mathcal{L} = \frac{1}{2} m (\dot{x}^2 + \dot{z}^2 - mgz = \frac{1}{2}m (\dot{\rho}^2 + \rho^2 \dot{\phi}^2) - mg \rho...

I need to find the extrema of f(x,y,z)=x+y+z subject to the restraints of x^2 - y^2 = 1 and 2x+z = 1. So the gradient of f equals (1,1,1) = lambda1(2x,-2y,0) + lambda2(2,0,1). Solving for the lambdas I found that lambda1 = -1/(2x) = -1/(2y), or x=y. But this isn't possible if x^2 - y^2 = 1...

I'm stuck on the following question "Find the maximum and minimum values of f(x,y,z) = x^2y^2-y^2z^2 + z^2x^2 subject to the constraint of x^2 + y^2 + z^2 = 1 by using the method of lagrange multipliers. Write the 4 points where the minimum value is achieved and the 8 points where the...

Hi all, I was wondering how to go about solving an optimization problem for a function f(x,y,z) where the two constraint equations are given by: a is less than or equal to g(x,y,z) is less than or equal to b (a and b are two distinct numbers) h(x,y,z) is less than or equal to c (c is...

Help Please! Studying for test : Lagrange Multipliers! Good morning all. I am having trouble with the next step to the following problem: Q.Find all realtive extrema of x^2y^2 subject to the constraint 4x^2 + y^2 = 8. g(x)= x^2y^2 f(x) = 4x^2 + y^2 = 8. the gradiant of f = <8x,2y>...

Hi, I'm having trouble with the following question. Q. Find the maximum and minimum of the function f(x,y) = x^2 + xy + y^2 on the circle x^2 + y^2 = 1. I started off by writing: Let g(x,y) = x^2 + y^2 then \nabla f = \lambda \nabla g,g\left( {x,y} \right) = 1 \Rightarrow 2x + y...

Lagrange Problem redux -- super urgent... See the attachment to help you visualize this. A rod of length L and mass m is povoted at the origin and swings in the vertical plane. The other end of the rod is attached/pivoted to the center of a thin disk of mass m and radius r. OK, I know that...

We have a rod of length L and mass M pivoted at a point at the origin. This rod can swing in the vertical plane. The other end of the rod is pivoted to the center of a thin disk of mass M and radius R. Derive the equations of motion for the system. I have attached a drawing :) If you...

LaGrange Multipliers! Help! Use the Lagrange multiplier method for 3 variables to find the points on the surface 3xy-z^2=1 that are closest to the origin. I tried using the gradient= lamda(granient) and ended up getting (-3/2,0,-1). but i think i did it way wrong. Can someone please help...

Hi, I would appreciate if anyone can help me out with the following question. I've been asked to find the point on the surface z = xy + 1 nearest to the origin by using the Lagrange Multiplier method. But all the examples I've been given in class and for coursework gave you the constraint...

Find the shortest and longest distance from the origin to the curve x^2 + xy + y^2=16 and give a geometric interpretation...the hint given is to find the maximum of x^2+y^2 i am not sure what to do for this problem thanks

I can't understand what the question is asking~ hope somebody can help me~ A particle of mass m moves in a plane under the influence of Newtonian gravitation force, described by the potential V(r) = - GmM/r (symbol in conventional meaning) Now introduce a new variable u(theta) = 1/r(theta)...

For the proof of lagrange multipliers, it is based on the assumption that the function you are optimizing, f(x,y,z), takes on an extreme value at the point (x0,y0,z0), and that any curve that passes through this point has the tangent vector perpendicular to the gradient vector. That seems fair...

This problem was given in my calc class during the semester, "Find the lowest point on the intersection of the sphere x^2+y^2 +z^2 = 30 and the cone 2*x^2 +y^2 = c^2". I don't know how to solve this problem with lagrange multipliers. How is it done? Thanks! Callisto

I'm not entirely sure what the english terms are for some of the things I'm about to say but i hope it's clear what I mean exactly. I'n my handbook the theorom is said to be: Say G is a part (wich is open) of R^n, f and g are functions from G to R (f:G->R, g:G->R) and both are differentiable...

Hello, I'm looking for a good Dynamics Book. I got Engineering Mechanics: Dynamics by Andrew Pytel and Jaan Kiusalaas, but it's fairly introductional, i also got Classical Mechanics by Goldstein, which is advanced. I am looking for intermediate level. I am looking mainly to learn the Lagrange...

1/sin(phi) * d/d\phi(sin(phi) * du/d\phi) - d^2u/dt^2 = -sin 2t for 0<\phi < pi, 0<t<\inf Init. conditions: u(\phi,0) = 0 du(\phi,0)/dt = 0 for 0<\phi<pi How do I solve this problem and show if it exhibits resonance? the natural frequencies are w = w_n = sqrt(/\_n) =2...

In my BC calc class, we just finished working through most of series and sequences, and as we were reviewing years past free response questions on the topic, and in 2004, they dropped a lagrange error analysis. I've been looking at different explanations, but I'm not getting the concept. It...

Hey guys, i need some help with this problem. It goes as follow: Find the global max and min valves of the fuction z=x^2+2y^2 on the circle x^2+y^2=1. Ok and here is what i have done. I found the derivites and have done (K is the lagrange constant) 2x=2xK K=1 4y=2yK K=2 Then i set...

Greetings all, Find the max and min values of f(x,y.z)=3x-y-3z subject to x+y-z=0, x^(2)+2z^(2)=1 can anybody help me get this problem started. thanks

Use Lagrange Multipliers to prove that the triangle with the maximum area that has a given perimeter p is equilateral. [Hint: Use Heron’s formula for the area of a triangle: A = sqrt[s(s - x)(s - y)(s - z)] where s = p/2 and x, y, and z are the lengths of the sides.] I have no idea how to do...

It has been a while and trying to brush up on LaGrange points. I want to find the highest and lowest points on the ellipse of the intersection of the cone: x^2+y^2-z^2 ;subject to the single constraint: x+2y+3z=3 (plane). I want to find the points and I am not concerned with the minimum and...

Find the points at which the function f(x,y,z)=x^8+y^8+z^8 achieves its minimum on the surface x^4+y^4+z^4=4. I know 8x^7=(lamda)4x^3 8y^7=(lamda)4y^3 8z^7=(lamda)4z^3 x^4+y^4+z^4=4 Case1: x not equal to 0, y not equal to 0, and z not equal to 0 I get 3(4th root of 4/3 to the eigth)...

-------------------------------------------------------------------------------- Ok this is the question I had on a test today: given this constraint equation z^2-xy+1=0 find the min. distance from the origin using Lagrange method. so basically you use D^2=x^2+y^2+z^2 as the other...

i have been given a problem involving a pendulum, where its support point is accelerating vertically upward. The period of the pendulum is required. Anybody have any idea how to start this one? is it not just 2pi(L/g-a)^1/2?