Tue 11/11

MAIN POINTS
6.5 defines Newton's law, then defines potential energy within the motion equation to show that the total energy is conserved. This makes it a conservative system. A conservative system, by definition, cannot have attracting fixed points. Ex. 6.5.3 shows the energy surface, which seems to be a convenient way of generalizing the potential diagram to 3 dimensions.

Reversible systems work the same when time is increased as when it is decreased... more precisely, thy are invariant as t -> -t and y -> -y. Example 6.6.1 is crazy looking. We are given more terminology with names about trajectories and saddles (could we possibly get a handout that distinguishes all of the different trajectory/saddle terms we've encountered so far?)

CHALLENGES
I don't understand the concept of a the homoclinic orbit... What does the text mean when it says 'centers are more robust when the system is conservative"? (p 163).

On p.165 they say curves "sufficiently close to the origin" are closed. I understand the logic based on symmetry... but is there a closed curve for every reversible system? Do you never see completely divergent behavior?

REFLECTION
Where do reversible systems show up in the real world? Potential energy/velocity are the main example of conservative systems... in this idealized model, does this mean a trajectory will always be moving, because no attracting fixed points are allowed? So.. a marbe would always be rolling around the energy surface...