ble, it reflects elastically, so the magnetic field does
reflection law. A peculiar feature of magnetic billiards
irreversibility: if one changes the velocity to the oppos
charge will not traverse its trajectory backward (unles
Remark 1.17. Classical mechanics and geometrical op
in this chapter, are intimately related. The configurati
of mechanical systems are extremals of a variational pri
to the trajectories of light. In fact, mechanics can be
kind of geometrical optics; this was Hamilton's approac
(see  for details). The brachistochrone problem is a
of this optics-mechanics analogy.
JEquivalently, one may consider billiards subject to the actio
related to rotation of the Earth.