A generalized Kowalevski Hamiltonian and new integrable cases on e(3) and so(4). 1 A new integrable case for the Kirchhoff equation. The Kirchhoff equations (see for example [1]) for the motion of a rigid body in an ideal fluid read as follows M t = M × ∂H ∂M + Γ × ∂H ∂Γ , Γ t = Γ × ∂H ∂M ,

Motivated by the approach to Laplacian on undirected weighted graphs, we provide a setting for general point of view Kirchhoff type divergence and Laplace operator built trivial gradient $f(y)-f(x)$ order zero. We consider some par