  We discuss the nonholonomic Chaplygin and the Borisov-Mamaev-Fedorov systems,
for which symplectic forms are different deformations of the square root from
the corresponding invariant volume form. In both cases second Poisson bivectors
are determined by $L$-tensors with non-zero torsion on the configurational
space, in contrast with the well known Eisenhart-Benenti and Turiel
constructions.
