  The dynamics of finite nonperiodic Toda lattice is an isospectral deformation
of the finite three--diagonal Jacobi matrix. It is known since the work of
Stieltjes that such matrices are in one--to--one correspondence with their Weyl
functions. These are rational functions mapping the upper half--plane into
itself. We consider representations of the Weyl functions as a quotient of two
polynomials and exponential representation. We establish a connection between
these representations and recently developed algebraic--geometrical approach to
the inverse problem for Jacobi matrix. The space of rational functions has
natural Poisson structure discovered by Atiyah and Hitchin. We show that an
invariance of the AH structure under linear--fractional transformations leads
to two systems of canonical coordinates and two families of commuting
Hamiltonians. We establish a relation of one of these systems with Jacobi
elliptic coordinates.
