Vlad Arnold's book on Mechanics

[homology]

Hey Folks,

Anyone here ever deal with V.Arnold's Book "Mathematical Methods of Classical Mechanics?" A friend of mine and I have started working through it and we have a question. First I'll state it then comment:

Problem: A mechanical system consists to two points. At the initial moment their velocities (in some inertial coordinate system) are equal to zero. Show that the points will stay on the line which connected them at the initial moment.

Now sure this is pretty obvious. But all we have to work with are

1) Space is 3D and time is 1D
2) Galileo's prin. of relativity (inertial frames are good and any frame moving uniformly with respect to an inertial frame is inertial)
3) Newton's prin. of determinacy (initial positions and velocities uniquely determine all the motions of a system.

Then Arnold develops the Galilean structure, the Galilean transformations and draws conclusions about Newton's equations as a result. If you're interested in helping out, I'll post some more. Again, our intuition says "Duh" (at least in terms of classical mech) but we don't have much to work with.


Thanks in advance!

Kevin

 

[Coelum]

... all we have to work with are

1) Space is 3D and time is 1D
2) Galileo's prin. of relativity (inertial frames are good and any frame moving uniformly with respect to an inertial frame is inertial)
3) Newton's prin. of determinacy (initial positions and velocities uniquely determine all the motions of a system.

...

Kevin

I'm not an expert but I believe we have something more than that. We have the hypothesys that the space is invariant under translation and rotation. Can the space be invariant under rotation if we break the initial rotational symmetry (e.g., by moving orthogonally to the joining line)?