Lagrange Definition and 542 Threads

Can anybody explain in simple and easy words "Lagrange Multiplier" What is it? and when it is used? i googled it but that was explained in much difficult words.

I'm trying to find out if Mars has any Lagrange Points - L1 and L2 specifically. A lengthy trawl through Google's webpages suggest that they may exist, although if so they would be extremely close to Mars, being gravitationally bound by Phobos and Deimos. Is this true? PS. Should Mars indeed...

Hey guys, looking to get some advice on satellite navigation. Can anyone recommend a nice textbook covering Newton, Kepler, Lagrange etc and their contributions to orbital motion. Also any textbooks on MATLAB or Maple examples of orbits - relativistic or Newtonian it doesn't matter. Not put off...

The Wiki article shows 5 Lagrange points. I can “see” how the points L1, L4 and L5 points would be balanced by the gravitation of the two bodies, but not the L2 and L3. For L2 and L3, it looks to me like the combination of the Sun’s and Earth’s gravity increase pull and make less stable. So...

Hello, When doing a little internet search today on generalized coordinates I stumbled on this document: http://people.duke.edu/~hpgavin/cee541/LagrangesEqns.pdf If you are willing, would you be so kind as to open it up and look at the top of (numbered) page 6? OK, so the very existence of...

Yes, that is a serious title for the thread. Could someone please define GENERALIZED COORDINATES? In other words (and with a thread title like that, I damn well better be sure there are other words ) I understand variational methods, Lagrange, Hamilton, (and all that). I understand the...

Homework Statement I am going to paste the problem word for word, so you can have all the exact information that I have: You’re part of a team that’s designing a rocket for a specific mission. The thrust (force) produced by the rocket’s engine will give it an acceleration of a feet per second...

Homework Statement We've got a line element ds^2 = f(x) du^2 + dx^2 From that we should find the geodesic equation Homework Equations Line Element: ds^2 = dq^j g_{jk} dq^k Geodesic Equation: \ddot{q}^j = -\Gamma_{km}^j \dot{q}^k \dot{q}^m Christoffel Symbol: \Gamma_{km}^j = \frac{g^{jl}}{2}...

Lately when doing a simulation for a quadrocopters most reports I've come across regarding modeling use Eulers equation of motion. That makes sense, as the quadrocopter is a body rotating in 3 dimensions. Then I tried to model the system using Lagrange equations instead but I don't get the...

Homework Statement Hi everybody! Here is a new Lagrange problem I am trying to solve, and I would like to have your opinion about my solution so far! A barbell composed of two masses ##m_1## and ##m_2##, idealised as particles and separated by a distance ##a## from each other, moves in the...

Homework Statement In this exercise, we are given a discrete Lagrangian which looks like this: http://imgur.com/TL0P61r. We have to minimize the discrete S with fixed point r_i and r_f and find the the discrete equations of motions. In the second part we should derive a discrete trajectory for...

Homework Statement Homework Equations L = T-V The Attempt at a Solution I got a forumla for the lagrangian as

Hi all I am facing a problem and I hope that you can give me a hand. Here I describe the situation I am working on a digitizer that can detect the pen position by measuring the antennae energy that are placed in a grid fashion. To get the x coordinate of the pen I measure the energy of three...

Hello, How can I use Lagrange Multipliers to get the Extrema of a curve f(x,y) = x2+4y2-2x2y+4 over a rectangular region -1<=x<=1 and -1<=y<=1 ? Thanks

Homework Statement This was supposed to be an easy question. I have a question here that wants you to describe a yoyo's acceleration (in one dimension) using Lagrangian mechanics. I did and got the right answer. Now I want to use Hamilton's equations of motion but I get a wrong number. Here is...

Homework Statement Im trying to understand the Legendre transform from Lagrange to Hamiltonian but I don't get it. This pdf was good but when compared to wolfram alphas example they're slightly different even when accounting for variables. I think one of them is wrong. I trust wolfram over the...

Homework Statement The cylinder x^2 + y^2 = 1 intersects the plane x + z = 1 in an ellipse. Find the point on the ellipse furthest from the origin. Homework Equations $f(x) = x^2 + y^2 + z^2$ $h(x) = x^2 + y^2 = 1$ $g(x) = x + z = 1$ The Attempt at a Solution $\langle 2x, 2y, 2z \rangle...

Why do displaced paths need to satisfy the equations of constraint when using the method of Lagrange multiplier? I thought that with the multiplier, all the coordinates are free and hence should not be required to satisfy the equations of constraint. Source...

Hello! (Wave) With use of algebra I want to prove the Lagrange property:For any real numbers $x_1, \dots, x_n$ and $y_1, \dots, y_n$, $$\left( \sum_{i=1}^n x_i y_i\right)^2=\left(\sum_{i=1}^n x_i^2 \right)\left(\sum_{i=1}^n y_i^2 \right)- \sum_{i<j} (x_i y_j-x_j y_i)^2$$ Could you give me a...

Hi all, I'm working on a project to control the angles of a beam(purple) with a quadcopter(orange),see figure below. The angles for both the ground-beam and beam-quadcopter will be measured with joysticks, so only roll and pitch angles will be measured and the yaw rotation is fixed. To obtain...

With coordinates q en basis e ,textbooks use as line element : ds=∑ ei*dqi But ei is a function of place, as one can see in deriving formulas for covariant derivative. Why don't they use as line element the correct: ds=∑ (ei*dqi+dei*qi) Same question in deriving covariant derivative,

Mod note: Moved from Homework section 1. Homework Statement Understand most of the derivation of the E-L just fine, but am confused about the fact that we can somehow Taylor expand ##L## in this way: $$ L\bigg[ y+\alpha\eta(x),y'+\alpha \eta^{'}(x),x\bigg] = L \bigg[ y, y',x\bigg] +...

Hello everyone! I'm currently trying to plot the effective potential for Sun-Jupiter system, to show the lagrangian points in this system. I've converted to a system of units where G=1, m_sun+m_jupiter=1 and R=1, whereby I get the following equation describing the effective potential of a third...

regarding question number 10, we have h = f + λg where g is the constraint (the ellipsoid) and f is the function we need to maximize or minimize (the rectangular parallelpiped volume), now my question : is it right that f is 8xyz ? i mean if we take f to be xyz not 8xyz and solved till we got...

Hi everybody; I am looking for the deduction of the euler lagrange equations (d/dt)(∂L/∂v)-(∂L/∂x) from the invariance of the action δ∫Ldt=0. Can someone please tell me where can I find It? Thanks for reading.

$\text{Let } L_{n,i}, i = 0,...,n, \text{be the Lagrange nodal basis at} x_0 < x_1<...<x_n$. Show that, for any polynomial $q \in P_n$ $$\sum_{i=0}^nq(x_i)L_{n,i}(x)= q(x)$$ I don't know how to begin this proof. I know what a lagrange polynomial is, but I am not sure how to begin. If someone...

I have a more philosophical question about the interpretation of a mathematical process. We have a chiral superscalarfield shown as partiell Grassmann Integral and transform it into a lagrange. where S and P are real components of a complex scalarfield and D and G are real componentfields of...

Hi, I have been trying to find some articles that would cover the Lagrange mesh method applied to the 1-D Schrödinger eqtn. - using the Laguerre mesh. I want to develop some fortran programs, for example building Lagrange functions, the kinetic energy matrix elements ... LMM is totally new to...

Hi, I have read this paper “Dynamic equations of motion for a 3-bar tensegrity based mobile robot” (1) and this one “Dynamic Simulation of Six-strut Tensegrity Robot Rolling”. 1) http://digital.csic.es/bitstream/10261/30336/1/Dynamic%20equations.pdf I am trying to implement a tensegrity...

Here is what we know from virtual work: $$ \delta W=\sum_{i=1}^N{\vec F_i\cdot\delta\vec r_{i}} $$ Where ##N## is the number of bodies in the system. I am considering a quadcopter, modeled as a rigid body so it is just one body and we have: $$ \delta W=\vec F\cdot\delta\vec r $$ My question...

I am trying to do go over the derivations for the principle of least action, and there seems to be an implicit assumption that I can't seem to justify. For the simple case of particles it is the following equality δ(dq/dt) = d(δq)/dt Where q is some coordinate, and δf is the first variation in...

According to this NASA factsheet (http://www.nasa.gov/pdf/664158main_sls_fs_master.pdf ) on the Space Launch System (SLS), NASA identifies missions to a Lagrange point as a possibility. From what I understand, a Lagrange point is simply a point where the gravitational fields of two massive...

www.youtube.com/watch?v=oW4jM0smS_E That's the video I'm referencing in particular, but 1 and 3 are necessary prereqs if you're new to the matter (as I am). He goes through and derives the product rule and power rule for polynomials using algebra. My question is this: why don't we teach...

Hello! I'd like to ask for help with one problem :) thank you in advance. 1. Write the equations for kinetic and potential energy for the pendulum with rectangular prism of size a*b*c (width, length, depth). With the Lagrange's equation get the equation of motion. The block is homogeneous...

Hello all I have this problem: Use Lagrange Multipliers to find the min and max of: \[f(x,y)=xy^{2}\] under the constraint: \[x-4y=1\] \[-1\leqslant x\leq 2\] My problem is: I know how to solve if \[-1\leqslant x\leq 2\] wasn't given. I calculate the Lagrangian function, find it's...

Homework Statement Find the equations of motion for both r and \theta of Homework Equations My problem is taking the derivative wrt time of and \dfrac{\partial\mathcal{L}}{\partial\dot{r}}=m \dot{r} \left( 1 + \left( \dfrac{\partial H}{\partial r}\right)^2 \right) The Attempt at a...

Hello Seniors, I have done BSc in Physics but couldn't take lectures of Classical Mechanics. I am Almost blind in this subject. Since it's a core course in Physics, so i need your help to understand the basics in this course. If anyone of you have any helping material/notes/slides etc which...

Hello. Do I need to grasp well the Lagrangian and Hamiltonian formulations in classical mechanics to go through quantum mechanics without struggles?

Use Lagrange multipliers to find $a,b,c$ so that the volume $V=\frac{4\pi}{3}abc$ of an ellipsoid $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$, passing through the point $(1,2,1)$ is as small as possible. I just need to make sure my setup is correct. $\triangledown...

Homework Statement A particle moves on the surface of an inverted cone. The Lagrangian is given by Show that there is a solution of the equations of motion where and take constant values and respectively Homework Equations The equations of motion and are (1) (2) So can be...

I am newly learning Lagrange formalism and I learned how to get the equation of motion for a simple pendulum using Lagrange in the spherical coordinate system. But I am unable to derive the same using the Cartesian system. If someone can please tell me what is wrong with the following...

Homework Statement Derive the equations of motion and show that the equation of motion for \phi implies that r^2\dot{\phi}=K where K is a constant Homework Equations Using cylindrical coordinates and z=\alpha r The kinetic and potential energies are...

I am trying to derive it but I am stuck at the boundary condition. What is this boundary comdition thing such that the value must be zero?

extremize $$S = \int \mathcal{L}(\mathbf{y}, \mathbf{y}', t) dt $$ subject to constraint $$g(\mathbf{y}, t) = 0 $$ We move away from the solution by $$y_i(t) = y_{i,0}(t) + \alpha n_i(t) $$ $$\delta S = \int \sum_i \left(\frac{\partial\mathcal{L} }{\partial y_i} - \frac{d}{dt} \frac{\partial...

Homework Statement My question is quite specific, but I will include the entire question as laid out in the text Consider the problem of minimizing the function f(x,y) = x on the curve y^2 + x^4 -x^3 = 0 (a piriform). (a) Try using Lagrange Multipliers to solve the problem (b) Show that the...

Suppose I have a function f(x,y) I would like to optimize, subject to constraint g(x,y)=0. Let H=f+λg, The extrema occurs at (x,y) which satisfy Hy=0 Hx=0 g(x,y)=0 Suppose the solutions are (a,b) and (c,d). If f(a,b)=f(c,d) , how do I determine whether they are maxima or minima?

In general, when dealing with mechanics problems using a function ##f(q1,q2,...)=0## that represent constraints one is minimizing the action ##S## while adding a term to the Lagrangian of the not-independent coordinates ##L + \lambda f ##. One can show that this addition doesn't change the...

Consider a holonomic system where I have ##n## not independent variables and one constraint ##f(q1,q2,...,qN,t)=0##. One can rewrite the minimal action principle as: ##\frac{\partial L}{\partial q_i} - \frac{d}{dt} \frac{\partial L}{\partial q'_i} - \lambda \frac{\partial f}{\partial q_i} = 0...

Homework Statement Derive the equation of motion for the system in figure 6.4 using Lagrange's equations [/B] Homework Equations m1=.5m m2=m strings are massless and in constant tension Lagrange=T-V The Attempt at a Solution I currently have the kinetic energy as .5m1y'12 + .5m2y'22 I am...

Hi! I need to figure out the Lagrange Equation for a rod or nail swinging from a horizontal plane. The thing is, that while it is swinging back and forth, the while nail is moving along the X axis as well. I was thinking to use 1/2mv^2+(1/2)Iø^2 . Any help would be appreciated! Thanks.