Interest in Areas of Classical Mechanics

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SUMMARY

Hamiltonian and Lagrangian mechanics are advanced formulations of classical mechanics that offer distinct advantages over Newtonian mechanics, particularly in solving complex problems and transitioning to quantum mechanics. These topics are typically introduced in upper division mechanics courses during the third or fourth year of university, following foundational studies in Newtonian mechanics. Essential mathematical prerequisites include a full calculus sequence, partial derivatives, and potentially differential equations. Recommended textbooks for these subjects include Fowles/Cassiday, Thornton/Marion, and Symon.

PREREQUISITES
  • Full calculus sequence
  • Partial derivatives
  • Differential equations (optional)
  • Introductory physics based on Newtonian mechanics
NEXT STEPS
  • Study Hamiltonian mechanics using the textbook by Thornton/Marion
  • Explore Lagrangian mechanics through Fowles/Cassiday
  • Review differential equations to support understanding of advanced mechanics
  • Investigate the transition from classical to quantum mechanics
USEFUL FOR

Students in physics, particularly those in upper division mechanics courses, educators teaching classical mechanics, and anyone interested in the mathematical foundations of advanced physics concepts.

Sho Kano
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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?
 
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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
 
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