  We discuss a non-Hamiltonian vector field appearing in consideration of a
partial motion of the Chaplygin ball rolling on a horizontal plane which
rotates with constant angular velocity. In two partial cases this vector field
is expressed via Hamiltonian vector fields using a non-algebraic deformation of
the canonical Poisson bivector on e^*(3). For the symmetric ball we also
calculate variables of separation, compatible Poisson brackets, algebra of
Haantjes operators and 2x2 Lax matrices.
