6 ms·

are there any unsolved problems in classical mechanics?

by dudeget 10y ago

Avshalom 10y ago
if you want to include fluid mechanics: https://en.wikipedia.org/wiki/Turbulence https://en.wikipedia.org/wiki/Turbulence https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc...
ulucs 10y ago
3-body problem is still unsolved if collisions are involved
- dnautics 10y ago
  there's still interesting issues of numerical accuracy in the point-mass case: E.G. is there a "good" way to calculate positions to arbitrary precision given starting conditions given in arbitrary precision, and what the relationship is.
dnautics 10y ago
I think the granular pile problem is still unsolved: Can you predict the cone angle of a pile of granular material given a small set of initial parameters?
antognini 10y ago
Absolutely. A lot of my thesis could be considered classical mechanics (orbital dynamics, specifically). A very old problem that is still open is the question of whether the solar system is stable. (Newton worked on this question 300 years ago.) The state of the art can only reliably integrate orbits for the next few million years. After that, numerical limitations and chaos make it hard to predict exactly what the dynamics in the far future will be. All we can do is make statistical predictions (which we hope are unbiased). The best predictions are that there is a ~1% chance that two planets will collide before the Sun dies. Here's a nice article: http://www.scholarpedia.org/article/Stability_of_the_solar_system http://www.scholarpedia.org/article/Stability_of_the_solar_s...
- aYsY4dDQ2NrcNzA 10y ago
  Does this count as having testable solutions?
aYsY4dDQ2NrcNzA 10y ago
I remember being told once that we don't have good simulation techniques for predicting the sounds produced by, for instance, the collision of two solid bodies. Lots of work has been done on modeling the kinematics and the optical appearance, but not on the audio side. I don't know if this is still true.
- pavel_lishin 10y ago
  Work has been done on this: https://www.youtube.com/watch?v=flOevlA9RyQ https://www.youtube.com/watch?v=flOevlA9RyQ https://www.youtube.com/watch?v=ZaFqvM1IsP8 https://www.youtube.com/watch?v=ZaFqvM1IsP8
augustl 10y ago
I heard somewhere that when we apply all our knowledge to compute the position of the moon, it is a couple of feet off when we measure it, and we don't know why. I have been trying to find a source for that, but I've failed. Perhaps someone reading this knows? :)

are there any unsolved problems in classical mechanics?

by dudeget 10y ago

are there any unsolved problems in classical mechanics?

if you want to include fluid mechanics: https://en.wikipedia.org/wiki/Turbulence https://en.wikipedia.org/wiki/Turbulence https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc...

ulucs 10y ago

3-body problem is still unsolved if collisions are involved

dnautics 10y ago
there's still interesting issues of numerical accuracy in the point-mass case: E.G. is there a "good" way to calculate positions to arbitrary precision given starting conditions given in arbitrary precision, and what the relationship is.

dnautics 10y ago

I think the granular pile problem is still unsolved: Can you predict the cone angle of a pile of granular material given a small set of initial parameters?

antognini 10y ago

Absolutely. A lot of my thesis could be considered classical mechanics (orbital dynamics, specifically). A very old problem that is still open is the question of whether the solar system is stable. (Newton worked on this question 300 years ago.) The state of the art can only reliably integrate orbits for the next few million years. After that, numerical limitations and chaos make it hard to predict exactly what the dynamics in the far future will be. All we can do is make statistical predictions (which we hope are unbiased). The best predictions are that there is a ~1% chance that two planets will collide before the Sun dies. Here's a nice article: http://www.scholarpedia.org/article/Stability_of_the_solar_system http://www.scholarpedia.org/article/Stability_of_the_solar_s...

aYsY4dDQ2NrcNzA 10y ago
Does this count as having testable solutions?

aYsY4dDQ2NrcNzA 10y ago

I remember being told once that we don't have good simulation techniques for predicting the sounds produced by, for instance, the collision of two solid bodies. Lots of work has been done on modeling the kinematics and the optical appearance, but not on the audio side. I don't know if this is still true.

pavel_lishin 10y ago
Work has been done on this: https://www.youtube.com/watch?v=flOevlA9RyQ https://www.youtube.com/watch?v=flOevlA9RyQ https://www.youtube.com/watch?v=ZaFqvM1IsP8 https://www.youtube.com/watch?v=ZaFqvM1IsP8

augustl 10y ago

I heard somewhere that when we apply all our knowledge to compute the position of the moon, it is a couple of feet off when we measure it, and we don't know why. I have been trying to find a source for that, but I've failed. Perhaps someone reading this knows? :)