Lecture_03-hanging chain ¶

hanging chain variational solution

In this video, you see how to derive the equilibrium position of a complex system of parts.

The Lagrange equation is \(\frac{\partial F}{\partial y}-\frac{d}{dx}\left(\frac{\partial F}{\partial y'}\right) = 0\) for a functional, \(F=F(x,y,y')\). Show that if \(F = F(y,y')\), we can solve the first-order ODE: \(F-y'\frac{\partial F}{\partial y'}=constant\) *
There are a lot of steps in solving an engineering problem like this. What are the main three outputs from these steps:
1. Define equations?
2. Variational calculus (IBP and “trick”)?
3. solving the ODE?

Advanced Dynamics