Lagrange Definition and 510 Threads

Homework Statement A uniform circular cylinder of mass `m' (a yo-yo) has a light inextensible string wrapped around it so that it does not slip. The free end of the string is fastened to a support and the yo-yo moves in a vertical straight line with the straight part of the string also...

Homework Statement A uniform solid cylinder of mass `m' and radius `a' rolls on the rough outer surface of a fixed horizontal cylinder of radius `b'. Let `theta' be the angle between the plane containing the cylinder axes and the upward vertical (generalized coord.) Deduce that the cylinder...

Homework Statement Find the absolute maximum and minimum values for f(x,y) = sin x + cos y on the rectangle R defined by 0<=x<=2pi and 0<=y<=2pi using the method of Lagrange Multipliers. The Attempt at a Solution I don't know where to start in getting the constraint into something I...

Why when doing a Lagrange Multipler with two constraints, why do you add the gradients of the two constriant funcions and set it parallel to the function to be maximized...

Let F and f be functions of the same n variables where F describes a mechanical system and f defines a constraint. When considering the variation of these functions why does eliminating the nth term (for example using the Lagrange multiplier method) result in a free variation problem where it...

Homework Statement Consider the problem of finding the points on the surface xy+yz+zx=3 that are closest to the origin. 1) Use the identity (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx) to prove that x+y+z is not equal to 0 for any point on the given surface. 2) Use the method of Lagrange...

Homework Statement Use Lagrange Multipliers to find the Maximum and Minimum values of f(x,y) = x2-y. Subject to the restraint g(x,y) = x2+y2=25 Homework Equations gradient f(x,y)= gradient g(x,y) The Attempt at a Solution I have found the gradients of f and g to be f(x,y) =...

Homework Statement Let f be a function whose seventh derivative is f7(x) = 10,000cos x. If x = 1 is in the interval of convergence of the power series for this function, then the Taylor polynomial of degree six centered at x = 0 will approximate f(1) with an error of not more than a.)...

1. Homework Statement [/b] f\left(x,y\right) = x^2 +y^2 g\left(x,y\right) = x^4+y^4 = 2 Find the maximum and minimum using Lagrange multiplier Homework Equations The Attempt at a Solution grad f = 2xi +2yj grad g= 4x^3i + 4y^3j grad f= λ grad g 2x=4x^3λ and 2y=...

Hi, I am supposed to find the point on the cone z^2=x^2+y^2 which is closest to the point(9,12,5). here is my work: http://img27.imageshack.us/my.php?image=lagrange001.jpg Is it correct so far? If it is: I get stuck when trying to solve the equations z^2=x^2+y^2, x=9/12*y, and...

Homework Statement A uniform disk of mass M and radius a can roll along a rough horizontal rail. A particle of mass m is suspended from the center C of the disk by a light inextensible string b. The whole system moves in a vertical plane through a rail. Take as generalized coordinates x...

Hello, I am aware that magnetic forces can do no work. I am also aware that, in a conservative system, equations of motion that minimize the "action" (which are the true equations of motion) can be found with the euler-lagrange equation. The only information the euler-lagrange equation needs...

Could somebody explain to me how lagrange multipliers works in finding extrema of constrained functions? also, what is calculus of variations and lagrangian mechanics, and can somebody explain to me what the lagrangian function is and the euler-lagrange equation. And, i read something about...

Lagrange Polynomals are defined by: lj(t)= (t-a0) ...(t-aj-1)(t-aj+1)...(t-an) / (aj-a0)...(aj-aj-1)(aj-aj+1)...(aj-an) A) compute the lagrange polynomials associated with a0=1, a1=2, a2=3. Evaluate lj(ai). B) prove that (l0, l1, ... ln) form a basis for R[t] less than or equal to n...

help me out on this proble i am confuse a sport center is to be constructed.it consists of a rectangular region with a semicircle ach end .if the perimater of the room is to be a 500 meter running truck find the dimetion that will make the area as large as possible. i can find if the...

Hi people, here's my problem: A uniform, flexible rope of length D, mass M, hangs off a frictionless table-top of height greater than D. The length of the section of rope hanging off is A. Gravity accelerates the part of the rope that is hanging off, so the length of the hanging part increases...

Homework Statement A disk moves on an inclined plane, with the constraint that it's velocity is always at the same direction as it's plane (similar to an ice skate, maybe). In other words: If \hat{n} is a vector normal to the disk's plane, we have at all times: \hat{n} \cdot \vec{v} = 0. Also...

Homework Statement suppose that H and K are subgroups of a group G such that K is a proper subgroup of H which is a proper subgroup of G and suppose (H : K) and (G : H) are both finite. Then (G : K) is finite, and (G : K) = (G : H)(H : K). **that is to say that the proof must hold for...

Homework Statement Find the maximum and minimum values of f = (x-1)^2 + (y-1)^2 on the boundary of the circle g = x^2 + y^2 = 45. Homework Equations f=(x-1)^2 + (y-1)^2 g=x^2+y^2=45 gradf(x,y)=lambda*gradg(x,y) The Attempt at a Solution gradf(x,y)=<2x-2,2y-4>...

Use Lagrange Multipliers to find the maximum and minimum values of f(x,y)=x^{2}y subject to the constraint g(x,y)=x^{2}+y^{2}=1. \nablaf=\lambda\nablag \nablaf=<2xy,x^{2}> \nablag=<2x,2y> 1: 2xy=2x\lambda ends up being y=\lambda 2: x^{2}=2y\lambda ends up being(1...

Homework Statement Point P(x,y,z) lies on the part of the ellipsoid 2x^2 + 10y^2 + 5z^2 = 80 that is in the first octant of space. It is also a vertex of a rectangular parallelpiped each of whose sides are parallel to a coordinate plane. Use Method of LaGrange Multipliers to determine the...

[SOLVED] Determining Local Extrema with Lagrange Homework Statement Find local extram of f(x,y,z) = 8x+4y-z with constraint g(x,y,z) = x^2 + y^2 + z^2 = 9 Homework Equations \nabla f(x,y,z) = \lambda g(x,y,z) The Attempt at a Solution So I did the partial derivatives for F and...

Does the Klein-Gordon Lagrange density maximize or minimise the solution of the Klein-Gordon equation?

I know this is supposed to go in the HW forum but its not working there so I'm trying it here, and I'm actually running into the same problem with another problem AGAIN. Someone tell me if I am doing this right: --- \nablaHomework Statement Find the extrema of f(x,y)=x-y ; subject to...

Homework Statement Use lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. f(x,y) = x+3y, x2+y2≤2 Homework Equations grad f = λ grad g The Attempt at a Solution to find critical points in the interior region...

How to solve this problem? : Consider two particles of masses m1 and m2. Let m1 be confined to move on a circle of radius a in the z = 0 plane, centered at x = y = 0. Let m2 be confined to move on a circle of radius b in the z = c plane, centered at x = v = 0. A light (massless) spring of...

Homework Statement A particle of mass, m1, is constrained to move in a circle with radius a at z=0 and another particle of mass, m2, moves in a circle of radius b at z=c. For this we wish to write up the Lagrangian introucing the constraints by lagrange multipliers and solve the following...

Lagrange mult. ---finding max Homework Statement [/b] probability mass function is given by p(x1,...,xk; n, p1,... pk) := log (n!/x1!...xk!) p1^x1 p2^xk Here, n is a fixed strictly positive integer, xi E Z+ for 1 < i < k, \Sigma xi=n, 0 <pi <1, and \Sigma pi=1 The maximum...

Homework Statement Prove a \times (b \times c) = (a * c)b - (a*b)c For orthagonal coordinates, a,b,c Homework Equations Cross Product and Dot Product The Attempt at a Solution I thought about expanding both sides out and proving they are equal, but I just realized that the...

I'm trying to follow the idea behind Lagrange multipliers as given in the following wikipedia link. http://en.wikipedia.org/wiki/Lagrange_multipliers I follow the article right up until the point where it goes: 'To incorporate these conditions into one equation, we introduce an...

Homework Statement Using the method of lagrange multipliers, find the points on the curve 3x² - 4xy + 6y² = 140 which are closest and furthermost from the ORIGIN and the corresponding distances between them The Attempt at a Solution I have done roughly half the question but appear to be...

can anybody please clearly explain me the difference between these two frames of reference with few examples. my exames are closing up. please help me.

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is...

find min/max: f(x,y)=xy with constraint being 4x^2+9y^2=32 [gradient]f=[lambda]gradient g The Attempt at a Solution I thought I understood the Lagrange problems, but I can't seem to get the minimum right on the last few problems. I get x=+/-2 and then plug back into find y, then I use my...

I have used this method quite a lot but I have never completely understood the proof. The only book I have that provides a proof is Shifrin's "Multivariable Mathematics" which I find kind of confusing. Stewart's "proof" is more or less just geometric intuition. Does anyone know of a book that...

Homework Statement i needed to find the max and min possible volume for a box with edges that = 200cm and surface area that = 1500cm^2 using Lagrange multipliers.Homework Equations edges: 4x + 4y + 4z = 200cm Area: 2xy + 2xz + 2yz = 1500 cm^2 Volume = xyzThe Attempt at a Solution i brought it...

Hello everyone! I'm trying to find the relation between the lagrangian density and the hamiltonian, does anyone know how they are related? I also need a reference where I can find the relation. Thanks!

Hello: Problem1: The temp of the circular plate D= {(x1,x2) | x1^{2} + x2^{2} \leq 1} is given by T=2x^{2} -3y^{2} - 2x. Find hottest and coldest points of the plate. Problem 2 Show that for all (x1,x2,x3) \in R^{3} with x1>0, x2>0, x3>0 and x1x2x3 = 1, we have x1+x2+x3 \geq3...

Hi, Why is -BEi used instead of +BEi as the lagrange multiplier for indistinguishable particles? How is it justified? I've been reading a book about statistical mechanics and it introduces lagrange multipliers first for distinguishable particles- it has ln(ni) + a + BEi = 0. (where a is...

hi everyone! I'm having difficulty figuring this problem out. so here goes: f(x) = sin(x) Use the Lagrange formula to find the smallest value of n so that the nth degree Taylor polynomial for f centered at x = 0 approximates f at x = 1 with an error of no more that 0.001. whatever help...

We're suppose to minimize f(x,y,z)=x^2+y^2+z^2 subject to 2x+y+2z=9. I only ever remember learning how to do f(x,y) would it be the same equation? Thus, f(x,y,\lambda) = f(x,y) + \lambda g(x,y)? Meaning f(x,y,z,\lambda) = x^2+y^2+z^2 + \lambda (2x+y+2z-9) and then continue solving for each...

http://www.geocities.com/asdfasdf23135/advcal29.JPG I am wondering whether the above statement is true. "A necessary condition for the constrained optimization problem to have a GLOBAL min or max is that..." Should the word local replace global? I am confused about the method of...

hi all , i am new at this forum , so i don't exactly know the rules about the topics and their sorting i am self studying lagrange dynamics. so my question is : when writing lagrange equations for aparticle ,& the particle is in conformity with the constraints...

http://img151.imageshack.us/img151/5562/updatequicklyte1.jpg how would i solve it using MATLAB ? I tried many times but i didnt get the same answer may anyone help me please ?

I am a physics student just finishing my sophomore year, and i was looking into what i could expect in upcoming intermediate mechanics. I noticed that Lagrange mechanics seems to be a big topic, and that i need to understand it to move forward in my studies. Being too impatient to wait for the...

(1) f(x,y,z)=x+2y (2) x+y+z=1 (3) y^2+z^2=4 1=\lambda 2=\lambda+2y\mu 0=\lambda+2z\mu u=\frac{1}{2y} y=\pm\sqrt2 \ \ \ z=\pm\sqrt2 Plugging into equation 2 to solve for x. How do I know to use either y=\sqrt 2 \ \mbox{or} \ y=-\sqrt2 ... similarly with my values for z. edit: NVM, I'm an...

Homework Statement A uniform chain of length L and mass M is constrained to move in a frictionless tube. Initially a fraction (1-f0) of the chain rests in a horizontal section of the tube. The remaining fraction f rests in a section of the tube that is inclined downward from the horizontal at...

I'm trying to follow a professor's notes for finding Christoffel symbols for a two-sphere. He gives the following two equations: The Lagrangian for a two sphere:L = \left( \frac{d\theta}{ds} \right)^2 + sin^2\theta \left( \frac{d\phi}{ds} \right)^2 The Euler Lagrange equation: \frac{d}{ds}...

http://img100.imageshack.us/img100/9016/linalggp1.jpg for (a): does that mean i must compute l0(t), l1(t) and l2(t), and i wasn't sure how to do this with the lagrange polynomial formula given, so i found one online and did it, I'm not sure if this is correct, but my l0(t) looks like this: =...

[SOLVED] Euler Lagrange Equation Hi there , I am missing a crucial point on the proof of Euler Lagrange equation , here is my question : \frac{\partial f}{\partial y}-\frac{d}{dx}\left(\frac{df}{dy^{'}}\right)=0 (Euler-Lagrange equation) If the function "f" doesn't depend on x explicitly...