The forum discussion centers on selecting topics for an essay in classical mechanics, highlighting the Lagrangian and Hamiltonian formulations as key areas of interest. Participants suggest various topics, including the Legendre transformation, the three-body problem, and the brachistochrone problem. The discussion emphasizes the beauty of classical mechanics, particularly through the lens of energy descriptions and their implications for motion. Additional suggestions include exploring the Nambu-Goto action in special relativity and Noether's Theorem, showcasing the breadth of potential essay subjects.
PREREQUISITESStudents of physics, educators in classical mechanics, and anyone interested in writing scientific essays on advanced mechanics topics.
First, welcome to PF!SaintRodriguez said:I was wondering if someone can telling me a topic about classical mechanics which I can write an essay. First I thought to write about Legendre transformation, but I guess that is very general. Also, if someone can tell me some tips to write an scientific essay I'll be so glad.
Thank you very much!jedishrfu said:The most magical part of Classical Mechanics has to be the Lagrangian formulation. In Susskind's book on Classical Mechanics, he derives Newton's third law, F=ma from the Lagrangian formulation.
https://en.wikipedia.org/wiki/Lagrangian_mechanics
It's magical because by simply describing the potential and kinetic energies of a system, just scalar quantities, one can then determine the motion of the system.
Another topic would be the Hamiltonian formulation which became really useful in Quantum Mechanics.
https://en.wikipedia.org/wiki/Hamiltonian_mechanics
Lastly, an interesting problem would be cool:
- like the three-body problem as there are several exact solutions now. (https://en.wikipedia.org/wiki/Three-body_problem)
- the brachistochrone problem (https://en.wikipedia.org/wiki/Brachistochrone_curve)
- the problem of an object falling from a great height takes 9/11 of the time to fall the first half the distance. (Marion Chapter 5 problem #5 pg 205)
I'm sure there are youtube videos on these topics for further research.
… and I would argue it is at least as beautiful as Lagrangian mechanics. Just symplectic geometry and a single energy function.jedishrfu said:It's magical because by simply describing the potential and kinetic energies of a system, just scalar quantities, one can then determine the motion of the system.
Another topic would be the Hamiltonian formulation which became really useful in Quantum Mechanics.
malawi_glenn said:Here is a suggestion for a topic, useage of lagrangians in special relativity and then discuss the nambo-goto action (the action for a bosonic string on a world sheet)
As long as it is not quantum it is classical imo.jedishrfu said:Is this beyond Classical Mechanics ie bosonic strings? It looks really cool though. I found this writeup on wikipedia
Of course I may just be out of date since Strings weren't things when I was studying classical mechanics (in the Dark Ages before we even knew the universe was accelerating) but this seems way beyond what one would typically cover in a such a course.malawi_glenn said:jedishrfu said:Is this beyond Classical Mechanics ie bosonic strings? It looks really cool though. I found this writeup on wikipedia:
https://en.wikipedia.org/wiki/Nambu–Goto_action
Well depends on the scope of the essay. Is it to apply concepts from the course to a own choosen topic or something else? We still don't know? It would be very helpful to know the scope and the instructions for this project.bob012345 said:this seems way beyond what one would typically cover in a such a course.