Recent content by JukkaVayrynen

Yes. Solve in x-y-plane. But the most important thing to remember is the projection! Let da be surface element on f(x,y) and dA a surface element on x-y-plane. Then we have a relation da = dA \sqrt{\frac{\partial f(x,y)}{\partial x}^2 + \frac{\partial f(x,y)}{\partial y}^2 +1} (follows from the...

You can do it several ways. If you have some arbitrary surface, the trick is to project the surface to some simpler surface, for example the x-y-plane. With projection we have simpler integral in which we use dA, dA being infinitesimal surface element on our simpler surface, for example on the...

It's simple: you don't.

My understanding is that Lagrangian and Newtonian dynamics are very close to each other, Lagrangian just uses the fact that internal forces of the system don't affect the motion. Hamiltonian dynamics, based on the principle of variation, is something much more fundamental than the other two.

So the answer should be: y satisfies the boundary value problem y - y^3 + \frac{d^2 y}{dx^2} = 0, y(0) = 0, y(\infty) = 1?

Hello everybody. Sorry, I don't know how to use TeX yet, I couldn't find a testing zone. Problem: Let I = \int_0^\infty [(dy/dx)^2 - y^2 + (1/2)y^4]dx, and y(0) = 0, y(\infty) = 1. For I to be extremal, which differential equation does y satisfy? Solution: The condition is that \delta I...