Solving Classic Physics Problems with Euler, Bernoulli & Co.

[opsb]

I find it very interesting trying to solve the 'classic' kind of physics problems. The ones that Euler, the Bernouillis and co. bandied about, I've come across:

The shape of a hanging chain

The shape of a hanging elastic string

The brachistochrone (the shape of a wire such that a bead running along it gets from A to B in the shortest time possible in a gravitational potential)

The elastica (shape of a toothpick being gently bent)

Profile curve of a bubble film suspended between two identical rings

Profile curve of a meniscus (water in a glass beaker sort of thing)

The last one I created a thread on a while ago, and think I got to the bottom of it. Let me know if you get a solution.

Wondered if anyone knew any other good ones.

If not, have a crack at these, some of them are pretty tricky (and watch out - there's no general analytic solution to the elastica problem, so don't pull your hair out over it).

Hope I've posted this in the right place. They're clearly not homework questions.

 

[AndyW]

Hello there! First of all, I want to say that I completely agree with you - solving classic physics problems is not only interesting, but also very rewarding. It allows us to understand the fundamental principles and laws of physics in a more concrete way.

Regarding the problems you mentioned, I have come across some of them during my studies and research. The shape of a hanging chain, for example, is a classic problem in mechanics known as the catenary. It has practical applications in architecture and engineering, as it describes the shape of a cable or rope hanging freely under its own weight.

The brachistochrone problem, on the other hand, is a classic problem in calculus of variations. It was first solved by Johann Bernoulli in the 17th century and has since been studied extensively by mathematicians and physicists. It has applications in fields such as optimal control and robotics.

The elastica problem, as you mentioned, does not have a general analytic solution. However, it has been studied extensively using numerical methods and has applications in fields such as structural engineering and material science.

Apart from these, there are many other classic physics problems that are worth exploring. Some examples include the Kepler problem (describing the motion of planets around the sun), the double-slit experiment (explaining the wave-particle duality of light), and the harmonic oscillator (describing the motion of a mass attached to a spring).

In addition to these, there are also many interesting problems in modern physics that are still being studied and researched. These include the behavior of systems at the quantum level, the theory of relativity, and the search for a unified theory of physics.

Overall, I think it's great that you are interested in solving these classic physics problems. They not only enhance our understanding of the physical world but also challenge us to think critically and creatively. Keep exploring and don't hesitate to share your findings with others - who knows, you might just inspire someone else to delve into the fascinating world of physics.