# Classical Mechanics & Coordinates [closed]

1. What is the meaning generalised coordinates in Classical Mechanics?

2. How is Lagrangian formalism different from Hamiltonian formalism?

3. How are they related to Hamilton's Principle?

4. How are they related to Euler-Lagrange equation?

## closed as too broad by ja72, Brandon Enright, Kyle Kanos, John Rennie, Qmechanic♦Jan 6 '14 at 17:03

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• These are three separate and very general questions, each worth a discussion on their own. – ja72 Jan 6 '14 at 16:30
• You'll need to read some books to answer all these questions. – pppqqq Jan 6 '14 at 16:31
• A summary/sort of what we are trying to do will help before reading the book. – Isomorphic Jan 6 '14 at 16:32
• 1. a good mathematical description of a physical system, 2. velocities are replaced by momenta, 3. lets you find equations of motion in 2.'s, 4. is the application of 3.... – Robert Filter Jan 6 '14 at 16:38

I wll answer the first question to get the ball rolling.

Consider tracking a particle that is constrained on a 2D path. Can can choose to keep track of the $x$, $y$ coordinates separately (2 dof system) and include a constraint equation to keep the particle on the path.

Or

You can use a generalized coordinate which might be the distance along the path, or the polar angle, or whatever else makes sense to you and keeps the particle on the path with only 1 coordinate specification. Thus no need for an additional constraint equation.

That is the reason people use generalized coordinates, to reduce the system degrees of freedom acording to the constraints.