  We propose new concept of energy reservoir and effectively conserved
quantity, what enables us to treat dissipative systems along the lines of the
framework of Geometric Numerical Integration. Using this opportunity, we try to
confirm numerically if our idea is useful. Numerical experiments show good
qualitative behavior of integration technique for ODEs based on non-potential
Hamiltonian formalism. It occurs that rising accurracy is a difficult task due
to dissipative form of the system under scrutiny.
