- #1

SaintRodriguez

- 9

- 1

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter SaintRodriguez
- Start date

In summary: I'm thinking more like an intro to strings or quantum mechanics class.I don't believe this is beyond Classical Mechanics. A chain of balls falling freely from a height would be a good example.

- #1

SaintRodriguez

- 9

- 1

Physics news on Phys.org

- #2

jedishrfu

Mentor

- 14,937

- 9,401

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.

- #3

bob012345

Gold Member

- 2,107

- 922

First, welcome to PF!SaintRodriguez said:

Classical Mechanics is a large subject. Is this an essay for school? If so, what level of school? Have you had much mechanics and physics in school? What are you interested in?

- #4

SaintRodriguez

- 9

- 1

- #5

SaintRodriguez

- 9

- 1

Thank you very much!jedishrfu said:

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.

- #6

- 22,075

- 13,542

… 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.

- #7

malawi_glenn

Science Advisor

Homework Helper

- 6,735

- 2,457

Is it supposed to be 4 pages or 20 pages for instances?

Who is the intended audience, the teacher or fellow students?

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)

- #8

jedishrfu

Mentor

- 14,937

- 9,401

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)

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

and this Khan Academy video on Lagrangians:

- #9

malawi_glenn

Science Advisor

Homework Helper

- 6,735

- 2,457

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

More suggestions for OP:

- from particles to fields, scalar field theory

- explain the euler disc

- surfaces of soap bubbles

- #10

jedishrfu

Mentor

- 14,937

- 9,401

https://en.wikipedia.org/wiki/Frisbee

There's a thesis by Sarah Hummel on the motion and biomechanics of the frisbee that is quite cool

https://morleyfielddgc.files.wordpress.com/2009/04/hummelthesis.pdf

- #11

malawi_glenn

Science Advisor

Homework Helper

- 6,735

- 2,457

More ideas

Self falling chain fountain

Explaining two balls attached via rubber band rotation

Self falling chain fountain

Explaining two balls attached via rubber band rotation

- #12

bob012345

Gold Member

- 2,107

- 922

Of course I may just be out of date sincemalawi_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

- #13

malawi_glenn

Science Advisor

Homework Helper

- 6,735

- 2,457

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.

You can write down the action of and study the behaviour of non-quantum mechanical relativistic strings with just basic analytical mechanics. I had a friend who did his entire bachelor thesis on this. Did not touch quantization at all.

It is when you start to quantize it that you open the pandoras box with virasoro algebras, extra compactified dimensions, string charges,... and so on.

Another nice topic for essey work is of course Noethers Theorem.

- #14

jedishrfu

Mentor

- 14,937

- 9,401

The movement of a slinky.

Classical mechanics is a branch of physics that deals with the motion and behavior of macroscopic objects, such as planets, cars, and baseballs. It is based on the laws of motion and gravitation developed by Sir Isaac Newton in the 17th century.

Classical mechanics is important because it provides the foundation for understanding the motion of objects in our everyday lives. It also serves as the basis for more advanced fields such as quantum mechanics and relativity.

Some potential topics for an essay about classical mechanics could include the history of classical mechanics, the laws of motion and how they apply to real-world situations, the role of classical mechanics in modern physics, or the impact of classical mechanics on technology and engineering.

To choose a specific topic for your essay about classical mechanics, you can start by brainstorming ideas that interest you and relate to the subject. You can also research current developments and controversies in the field to find a topic that is both relevant and engaging.

There are many resources available for researching an essay on classical mechanics, including books, academic journals, websites, and scientific databases. You can also consult with a physics professor or visit your local library for additional resources and guidance.

- Replies
- 13

- Views
- 2K

- Replies
- 9

- Views
- 547

- Replies
- 3

- Views
- 4K

- Replies
- 2

- Views
- 3K

- Replies
- 2

- Views
- 963

- Replies
- 6

- Views
- 1K

- Replies
- 9

- Views
- 1K

- Replies
- 2

- Views
- 322

- Replies
- 1

- Views
- 2K

- Replies
- 3

- Views
- 2K

Share: