Unsolved problems in classical mechanics

[Oskiposki]

Are there any aspects of classical mechanics that are questionable or is all certain? I came across a article written by some known physicist who made it evident that there are still a lot of unsolved questions in classical mechanics. Unfortunetley I do not remember the name of the article or physisist as I read it very quickly. I who am a student thought that everything about classical mechanics was certain. I did not know of any other facts. It would be nice if someone could explain for me.

 

/Oskiposki

 

P.S. excuse my bad english.

[Qfwfq]

Your English is fine enough Oskiposki, it's understandable.

I came across a article written by some known physicist who made it evident that there are still a lot of unsolved questions in classical mechanics.

Perhaps referred to attractors and chaos?

 

There aren't really problems formally, afaik, only the fact that a dynamic system may be very complicated with limits on the feasibility of predictive calculation.

[xersan]

Recently I submitted a new unsolved problem. Please read under the thread < Lorentz's transformations have an unsolved problem>

[CraigD]

Are there any aspects of classical mechanics that are questionable or is all certain?

There are many unsolved problems in classical mechanics.

 

One very well known unsolved problem is known as “the 3 body problem”, or, more generally “the n-body problem”. It is:

Give the initial positions, velocities, and masses of 3 or more objects (they can be point masses, spheres of constant density, or whatever you wish), determine their exact position for a given time (either in the future, or in the past).

 

Despite what you may read (including in the wiki link above), this problem has nothing to do with chaos theory – you are given the system’s initial values with absolute precision. Still, to date, all solutions to this kind of problem are approximations – an exact, closed-form general solution has not been found.

[Erasmus00]

The three body has been shown to have no analytical solution. There simply aren't enough conserved quantities. Sundman, however, did put forth some arguments to show Jupiter is in a stable orbit. (restricted three body problem).

 

The n body problem where n is huge can be handled with a great deal of accuracy with statistical mechanics.

-Will

[Qfwfq]

Yes, of course, three or more bodies is a different matter from chaotic attractors, but "no analytical solution" isn't quite the same meaning as an "onsolved problem". Formally, when you define a system having certain canonical coordinates and a certain lagrangian or hamiltonian you're set. The differential equations can be integrated, even though this might not mean there being some general expressions of the solutions in terms of other things already defined, such as polynomials, sines, logs and whatnot. This is however a matter of calculus more than mechanics itself.

 

In calculus, a given f(x) will have a primitive up to a constant, regardless of whether or not you can find an expression that defines it better than just d F(x)/dx = f(x). If there are not such expressions, all you can do is pound salt. Or integrate numerically.

 

If you really think it straight, even when the solution can be expressed in terms of trig functions and the likes, are these really "exact" solutions? How do we know the value of tan 3pi/7?