Difference between Newtonian, Langrange, and Hamiltonian Mechanics

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Newtonian mechanics focuses on forces and vectors, while Lagrangian mechanics shifts the perspective to energy and scalars, simplifying problem-solving in complex systems. Hamiltonian mechanics further refines Lagrangian principles, transforming equations of motion into one-dimensional differential equations. Both Lagrangian and Hamiltonian mechanics are categorized as analytical mechanics, emphasizing a more conceptual and mathematical approach. While these advanced methods provide valuable insights, they may not always be practical for all physics problems. Overall, understanding these mechanics enhances comprehension of classical physics, but one should balance exploration with practical applications.
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Hey I was just wondering what the differences between the three forms of mechanics were. I've only studied basic Newtonian mechanics so I'm not really sure about the other two. Could anyone elaborate?
 
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They are not different in the sense you imply. Lagrangian mechanics is a further development of Newtonian dynamics, and Hamilton's work is based on Lagrange principles. So they form a progression.

It is a very large, important and fascinating field of study so it wouldn't be practical to teach it here. I recommend any decent book on classical mechanics, which will take you through the progression.
 
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Mechanics is mechanics. Lagrange and Hamilton mechanics are both known as analytical mechanics. The treatment is just more conceptual and more mathematical. It depends if you like formalism. Anyway, give it a try: sometimes it is easier (especially for systems with several degrees of freedom) to solve a problem with these tools rather than with a (in fact: several coupled) Newton equation, which quickly becomes cumbersome. Have a look to Landau or Goldstein books. To be honest, I should however say that analytical mechanics is nice, it gives a lot of insights and concepts, but it is not so useful in the end. Don't get too fascinated by this kind of stuff, and don't loose too much time (physics is wide !).
 
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diff. between these mechanics

see Newtonion mechanics deals with vectors like mom. and acc. but then came lagrangian mech. which deals in terms of energies which are scalars and hence equations are easy to solve. but these eqns. are second order differential eqns. .to improve on that and mke eqn. of motion a one dimensional diff. eqn. hamiltonian mech. is introduced.
 
Thanks, everyone, especially nandan!
 

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