Lagrange Definition and 541 Threads

It says you can not change with lenses the value L - radiance. Below I have an example where it proves that you can or where am I wrong? (I made L for 2D case, in 3D case everything the same - L2>L1)

Homework Statement On very hot days there sometimes can be a mirage seen hovering as you drive. Very close to the ground there is a temperature gradient which makes the refraction index rises with the height. Can we explain the mirage with it? Which unit do you need to extremalise? Writer the...

Homework Statement An object of mass m, and constrained to the x-y plane, travels frictionlessly along a curve f(x), while experiencing a gravitational force, m*g. Starting with the Lagrangian for the system and using the method of Lagrange multipliers, derive the equations of motion for the...

I have a few questions about the remainder theorem. 1: For series that "skip" terms (example: 1+x^2+x^4+x^6) the theorem says the n+1 derivative and x^(n+1)/(n+1)!. For example if you have 1 + x^2 where you know the next term would be x^4 you could treat it as a third order or a...

Hi! Does the Lagrange equation ONLY apply when the constraints are holonomic? What about the constraining forces acting on the system (i.e. normal force, or other perpendicular forces), do they make a system holonomic? What about the Lagrange equation with the general force on the right hand...

1. The problem statement I'm stuck with this problem which does not yield a solution. I feel as if I'm not formulating it correctly. Here it is described below. I've also written down the equations as they're easier to be read (attachment) This is something that I was doing with batteries and...

I know that The path Integral becames classical Lagrange (Classic Mechanics) how can it be turn it.

If metric is $$ds^2 = -f(x)dt^2 + g(x)dx^2 + 2l(x)dxdt $$ Then we have this Lagrangian: $$L= \frac{1}{2}(-f(x)\dot{t}^2 + g(x)\dot{x}^2 + 2l(x)\dot{x}\dot{t}).$$ The Euler-Lagrange equation for $$t$$ is: since $$t$$ is not there in the Lagrangian then $$\partial L/ \partial t=0$$ This implies...

Homework Statement [/B] A uniform solid ball of mass m rolls without slipping down a right angled wedge of mass M and angle θ from the horizontal, which itself can slide without friction on a horizontal floor. Find the acceleration of the ball relative to the wedge. 2. The attempt at a...

Hello, I am having a bit of trouble with the Lagrange multiplier method. My question is: Use the Lagrange multiplier method to find the extrema points of the distance from the point (1,2,3) to the surface of the sphere {x}^{2}+{y}^{2}+{z}^{2}=4. Find the possible values for of \lambda. This...

Homework Statement This is a real basic question I am sure. Maybe I just missed something. so in the book, t = the kinetic energy . only for a pendulum, they add kinetic energy of x dot squared, plus kinetic energy of y dot squared. Homework Equations T = 1/2 m v^2 a^2 + b^2 = c^2 The Attempt...

I am curios about trajectory programs (but not weather) the real particle movements.If you know How can I get it (but free) I will be happy Thanks

I want to know lagrange mechanics work in phase space or in coordinate system.Leonard Susskind talked about the least action and he said If we know two point we can define trajectory but I don't know the diagram that he drow its a phase space or coordinate system (x,y,z,t) 19 min or...

Homework Statement A simple pendulum of length ##b## and bob with mass ##m## is attached to a massless support moving vertically upward with constant acceleration ##a##. Determine (a) the equations of motion and (b) the period for small oscillations. 2. Formulas ##U = mgh## ##T = (1/2)mv^2...

(Sorry text is hard to read, please see attached document for an easier read) I am having trouble with #6, I'm not sure if what I have going on is entirely correct. Also #7 is a little confusing. Problem Statement & work done: For an object in orbit around a second, there are five LaGrange...

Homework Statement Find the maximum and minimum values of the function f(x, y) =49 − x^2 − y^2 subject to the constraint x + 3y = 10. The Attempt at a Solution ∇f = <2x,2y> ∇g = <1,3> ∇f =λ∇g 2x = λ 2y = 3λ 2x = 2y/3 x = y/3 y/3 + 3y = 10 y = 3 x = 1 f(1,3) = 39 Now that is the only...

I'm currently having some trouble, after the procedure of finding the actual values for the multipliers and the points, but how come can I figure out whether which points that I've collected are maxima, minima or just saddle ones. I've taken a look on lots of books, but I can't seem to find...

Homework Statement I need to optimize the following structure with respect to compliance P\cdot u_y. the constraint is that the volume of the truss must not exceed V_0. The design variables are the bar cross sections A_1,A_2,A_3 Homework Equations The mathematical programming problem I got is...

Homework Statement Hi guys I am new here and i really need help with this question. I've tried it multiple times but can't find all the critical points, help would be greatly appreciated. the question is as follows: Find the maximum and minimum values of w=4x-(1/2)y+(27/2)z on the surface...

Homework Statement Hey guys! So I have a Lagrangian with two coupled fields like so: \mathcal{L} = \frac{1}{2}(\partial_{\mu}\phi_{1})(\partial^{\mu}\phi_{1})...

Hi! I've been trying to find the equation of motion for the simple pendulum using x as the generalized coordinate (instead of the angle), but I haven't been able to get the right solution... Homework Statement The data is as usual, mass m, length l and gravity g. The X,Y axes origin can be...

This is a homework in mathematical modeling and optimization; we're up to Lagrange multipliers and shadow prices. 1. Homework Statement A manufacturer of PCs currently sells 10,000 units per month of a basic model. The cost of manufacture is 700$/unit, and the wholesale price is $950. The cost...

When considering the Lagrange point 1 in the Sun/Earth system, Does Lagrange Point 1 have any orbital velocity around Earth? I suspect a body at L1 has no orbital velocity around earth. But consider the Earth's position 6months later when it is opposite the sun. The Lagrange point would also...

in the problem f(x,y)=x^2+y^2 and xy=1, I get 2 as a local extrema and it is a min in the problem f(x1,x2...xn) = x1+x2..+xn (x1)^2+...(xn)^2=1 I get sqrt(n) and its a max. How do I know if these are max or min values? If I get more than two extrema, I just compare them and one's a max and the...

Homework Statement The system can pivot at point O and I am taking small angle approximations. I am trying to determine the Lagrangian, ##\mathcal{L} = T - U## for the following system: Homework Equations E-L equation with dissipation: ##\frac{\partial\mathcal{L}}{\partial q_i} -...

Homework Statement Sorry for the long derivation below. I want to check if what I derived is correct, I can't find it anywhere else, feel free to skip to the end. Thanks! I am confused by how to write the EL equations if I have multiple constraints of multiple coordinates. For example, let's...

The following Lagrange interpolation function is extremely useful. It can be used in just about any branch of science. I use it extensively in astronomical computations for such things as finding the dates and times of the seasons over thousands of years and phases of the moon at any given...

Homework Statement 7.27 ** Consider a double Atwood machine constructed as follows: A mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. The other end of this string supports a second similar pulley, over which passes a second string supporting a...

Hi, my professor asked me to proove the equations of motion of a problem. The equations that I need to find are in page 2 of the file https://docs.google.com/file/d/0BxOdCfkh6FqpUlY5TktpbDZTc2M/edit , equations 7 and 8. But, I'm having trouble with the exercise. I uploaded my attemps...

Homework Statement The Baraboo, Wisconsin plant of International Widget Co. uses aluminum, iron and magnesium to produce high-quality widgets. The quantity of widgets which may be produced using x tonnes of aluminum, y tonnes of iron and z tonnes of magnesium is Q(x,y,z) = xyz. the cost of raw...

Homework Statement I have to find the extrema of a given function with two constraints f(x,y,z) = x+y+z;x^2-y^2=1;2x+z=1 The Attempt at a Solution If I create a new function F then I have F(x,y,z,\lambda,\mu)=x+y+z-(x^2\lambda - y^2\lambda -\lambda) -(2x\mu + z\mu -...

Homework Statement Using Lagrange multipliers, find the max and the min values of f: f(x,y,z) = x^2 +2y^2+3x^2 Constraints: x + y + z =1 x - y + 2z = 2Homework Equations ∇f(x) = λ∇g(x) + μ∇h(x)The Attempt at a Solution Using Lagrange multipliers, I obtained the equations: 2x = λ + μ 4y =...

What is the Lagrange Mesh method?

i was given that D4=[e,c,c2,c3,d,cd,c2d,c3d] therfore D4=<c,d> is the subgroup of itself generated by c,d then they defined properties of D4 as follows ord(c)=d, ord(d)=2, dc=c-1d i am strugging to understand how they got that c4=e=d2

given that G is a finite group. 1) if H is a subgroup of G then |H| divides |G| 2) if a in G the ord(a)/|G| i could prove no 2 using no 1 where i said ord(a)=|<a>| and <a> is a subgroub of G so by 1 ord(a)/|G|how cAN I prove 1

Homework Statement f=xy^2 C: x^2 + y^2 = 3 Homework Equations The Attempt at a Solution I don't understand how he can say that x=0 is a solution in this one. Looking at the contours, there are no solutions for f if x=0.

Homework Statement I've thought of a problem to help me with Lagrange multipliers but have got stuck. Consider a particle of mass m moving on a surface described by the curve y = x2, the particle is released from rest at t = 0 and a position x = l. I'm trying to work out the EOM's but have...

Homework Statement Use Lagrange Multipliers to find the minimum value of f(x,y)=x^{2}+(y-1)^{2} that lie on the hyperbola x^{2}-y^{2}=1. Draw a picture to verify your final answer. Homework Equations \nabla f=\lambda \nabla C The Attempt at a Solution So I can find the critical...

Homework Statement At what points ##x## in the interval ##(-1,1]## can one use the Lagrange Remainder Theorem to verify the expansion ##ln(1+x)=\sum_{k=1}^{\infty} (-1)^{k+1}{\frac{x^k}{k!}}##Homework Equations The Attempt at a Solution Now I know that ##ln(1+x)=\sum_{k=1}^{\infty}...

Hi I am unable to find the proof of the Lagrange inversion formula as given in http://en.wikipedia.org/wiki/Lagrange_inversion_theorem#Theorem_statement I have searched all over the internet as well as the original paper published by Lagrange. Still could not find it. Any help would be...

Hello! I have a problem in classical mechanics that I'm unable to solve. Any help would be much appreciated since we have a partial exam tomorrow. :( Homework Statement There's a picture of the problem in the attachment A mass m, which is on a light rod (lenght d), is attached to a...

I have a system with one generalized coordinate, x. In the potential energy part of the lagrangian, I have some constants multiplied by the absolute value of x. That is the only x dependence the lagrangian has, so when I take the partial derivative of the lagrangian with respect to x (to get the...

Homework Statement The first block with mass m_1 slides without friction on a wedge which has an incline of angle \alpha. The wedged shaped block has a mass m_2 . The second block is also allowed to slide on a flat frictionless line. Find Lagrange's equations of motion. Homework...

Homework Statement A particle is confined to move on the surface of a circular cone with its axis on the vertical z axis, vertex at origin (pointing down), and half-angle α(alpha) a) write down the lagrangian in terms of spherical coordinates r and ø (phi) Homework Equations...

Homework Statement Find the extrema of f(x, y) = x2−2xy+ 2y2, subject to the constraint x2 +y2 = 1.Homework Equations ∇f(x,y) = λg(x,y)The Attempt at a Solution This is the work I have thus far: Letting g(x,y) = x2+y2-1, We obtain the following three equations from the Lagrange Multiplier...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Homework Statement Consider a bead of mass m sliding without friction on a wire that is bent in the shape of a parabola and is being spun with constant angular velocity w about its vertical axis. Use cylindrical polar coordinates and let the equation of the parabola be z = kp2. Write down the...

Here are the questions: I have posted a link there to this thread so the OP can view my work.

Hey :o ! Could you help me at the following exercise? $k, n \in \mathbb{N}$ $f(x)=cos(k \pi x), x \in [0,1]$ $x_i=ih, i=0,1,2,...,n, h=\frac{1}{n}$ Let $p \in \mathbb{P}_n$ the Lagrange interpolating polynomials of $f$ at the points $x_i$. Calculate an upper bound of the maximum error...

Homework Statement A ray of light enters a glass block of refractive index n and thickness d with angle of incidence θ1. Part of the ray refracts at some angle θ2 such that Snell's law is obeyed, and the rest undergoes specular reflection. The refracted ray reflects off the bottom of the block...