The requirements, posed on a system given
by the configuration coordinates
q(t) = (q^1(t), q^2(t), ...)
that
(1) they be subject to 2nd-order equations of motion:
q'(t) = v(t), v'(t) = a(q(t),v(t))
and
(2) have a classical configuration space at each time:
[q^i(t), q^j(t)] =
is nearly...