Interest in Areas of Classical Mechanics

[Sho Kano]

What are Hamiltonian/Lagrangian Mechanics and how are they different from Newtonian?
What are the benefits to studying them and at what year do they generally teach you this at a university?
What are the maths required for learning them?

 

[jtbell]

Newtonian mechanics is based directly on Newton's laws of motion. Lagrangian and Hamiltonian mechanics are alternative formulations which can be derived from Newtonian mechanics. It's easier to solve certain types of problems using them. They also provide a more "natural" or "direct" transition to quantum mechanics.

In the USA, students usually study them in an "upper division" mechanics course in the third or fourth year of university (sometimes second year), following a first-year introductory physics course based on Newtonian mechanics. Prerequisites are at least a full calculus sequence including partial derivatives, probably also a course in differential equations, depending on how the mechanics course is taught. Typical textbooks are Fowles/Cassiday, Thornton/Marion, and Symon.

https://en.wikipedia.org/wiki/Lagrangian_mechanics
https://en.wikipedia.org/wiki/Hamiltonian_mechanics