  Schroedinger equation on a Hilbert space ${\cal H}$, represents a linear
Hamiltonian dynamical system on the space of quantum pure states, the
projective Hilbert space $P {\cal H}$. Separable states of a bipartite quantum
system form a special submanifold of $P {\cal H}$.
  We analyze the Hamiltonian dynamics that corresponds to the quantum system
constrained on the manifold of separable states, using as an important example
the system of two interacting qubits. The constraints introduce nonlinearities
which render the dynamics nontrivial. We show that the qualitative properties
of the constrained dynamics clearly manifest the symmetry of the qubits system.
In particular, if the quantum Hamilton's operator has not enough symmetry, the
constrained dynamics is nonintegrable, and displays the typical features of a
Hamiltonian dynamical system with mixed phase space. Possible physical
realizations of the separability constraints are discussed.
