A fast and efficient numerical integration algorithm is presented for the problem of the secular evolution of the spin axis. Under the assumption that a celestial body rotates around its maximum moment of inertia, the equations of motion are reduced to the Hamiltonian form with a Lie-Poisson bracket. The integration method is based on the splitting of the Hamiltonian function, and so it conserves the Lie-Poisson structure. Two alternative partitions of the Hamiltonian are investigated, and second-order leapfrog integrators are provided for both cases. Non-Hamiltonian torques can be incorporated into the integrators with a combination of Euler and Lie-Euler approximations. Numerical tests of the methods confirm their useful properties of short computation time and reliability on long integration intervals.
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