Lagrange Definition and 510 Threads

A bit of a tough one! Find the maximum of ln x + ln y + 3 ln z on part of the sphere x^2 + y^2 + z^2 = 5r^2 where x>0, y>0 and z>0. I know I need to use Lagrange multipliers but how should I go about it? Any help would be appreciated thanks!

Lagrange' s equations of a suspended set of rods Three identical rods of length l and mass m are hinged together so as to form three sides of a square in a vertical plane. The two upper free ends are hinged to a rigid support. The system is free to move in its own plane. Use Lagrange' s...

Ok, there are two objects of mass m on a frictionless table. The 2 masses are connected to the other by a spring of spring constant k. One mass is connected to a wall with a spring of the same constant k. Solve for the motion using Lagrange' s equations. I used generalized coordinates x...

A smooth wire is bent into the form of a helix the equations of which, in cylindrical coordinates, are z=a*beta and r=b , in which a and b are constants. The origin is a center of attractive force, , which varies directly as the distance, r. By means of Lagrange’s equations find the motion...

I'm learning classical mechanics right now, and I have a question about the "initial definition" of the Lagrange function. In my book, it is only introduced as L=T-V, but in many cases this doesn't help a lot, since it's not obvious what T or V is. For example, how would I come to the Lagrangian...

Does anyone know of a good online resource on Lagrangian and Hamiltonian mechanics?

We have started to do Lagrange Multi. in my class and my book has a very short section on how to solve these. I was wondering if someone couls help. The problem is f(x,y)=x^2-y^2 with the constraint x^2+y^2=1. I have found the partial derv. but I am not sure on what else to do. Any help would...

A)How many LaGrange points does the Earth/Moon system have? B) How many are stable (no stationkeeping neccessary)? C) Roughly where are the stable points located? 1/2 point point for each answered correctly

Hi, I'm really stuck on this problem and I need some help?? Here's the question: The intersection of the elliptic paraboloid z=x^2+4y^2 and the right circular cylinder x^2+y^2=1. Use Lagrange multipliers to find the highest and lowest points on the curve of intersection. Your help will...

Find max and min value…f(x,y,z) =3x+2y+z; x2 + y2+z2 = 1 If g(x,y,z) = x2 + y2+z2 = 1 then what do I do next? I need help to further solve for this please? I am horrible at math and don't understand lagrange multipiers so can anyone better explain it to me and help me solve for difficult...