The conservative and dissipative terms of a 3D chaotic system are separated using Helmholtz theorem [F(x) = Fc(x) + Fd(X)]. How to find its Hamiltonian energy function (analytically and numerically)?

F(x) = Fc(x) + Fd(x), where F(x) is a 3D chaotic system, Fc(x) is a column vector with conservative field terms and Fd(x) is a column vector with dissipative field terms.

After using Helmholtz theorem it is obtained that

Fc(x)= full column vector;

Fd(x)= column vector with zero first row term.