A classical description of the two-electron atom, analogous to the quantum adiabatic hyperspherical channel approach, is presented. The classical problems, analogous to the quantum eigenvalue problem for the grand angular momentum operator, and the separated dynamical systems defined by each of the other constants of the motion of the non-interacting system are solved by using the Hamilton-Jacobi method. Some matrix elements of the Coulomb interaction terms of the Hamiltonian for doubly excited helium atoms using the Heisenberg correspondence principle are calculated.