  A first-principle continuum-mechanics expression for the rolling friction
coefficient is obtained for the rolling motion of a viscoelastic sphere on a
hard plane. It relates the friction coefficient to the viscous and elastic
constants of the sphere material. The relation obtained refers to the case when
the deformation of the sphere $\xi$ is small, the velocity of the sphere $V$ is
much less than the speed of sound in the material and when the characteristic
time $\xi/V$ is much larger than the dissipative relaxation times of the
viscoelastic material. To our knowledge this is the first ``first-principle''
expression of the rolling friction coefficient which does not contain empirical
parameters.
