  We present a new derivation of Hamilton's equations that shows that they have
a symmetry group Sp(2n) *s H(n). Sp(2n) is the symplectic group and H(n) is
mathematically a Weyl-Heisenberg group that is parameterized by velocity, force
and power where power is the central element of the group. We present a new
derivation of Hamilton's equations that shows that they have a symmetry group
Sp(2n) *s H(n). The group Sp(2n) is the real noncompact symplectic group and
H(n) is mathematically a Weyl-Heisenberg group that is parameterized by
velocity, force and power where power is the central element of the group. The
homogeneous Galilei group SO(n) *s A(n), where the special orthogonal group
SO(n) is parameterized by rotations and the abelian group A(n)is parameterized
by velocity, is the inertial subgroup.
