Homework Statement
The Lagrange method does work for some velocity dependent Lagrangian. A very important
case is a charged particle moving in a magnetic field. The magnetic field can be represented as a "curl" of a vector potential ∇B = ∇xA . A uniform magnetic field B0 corresponds to a
vector...
This means that the Lagrangian is independant of the coordinate system. And this makes sense, because a coordinate system is nothing physical and is arbitrary.
So, this means that the Lagrangian is universal? In other words, it works for any coordinate system.
Homework Statement
The problem asked us to show that the Euler-Lagrange's equations are invariant under a point transformation q_{i}=q_{i}(s_{1},...,s_{n},t), i=1...n. Give a physical interpretation.
Homework Equations
\frac{d}{dt}(\frac{\partial L}{\partial \dot{s_{j}}})=\frac{\partial...