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Relativity in Astrometry, Celestial Mechanics and Geodesy
General theory of orbital and rotational motion of celestial bodies. Precise and fast computation of special functions for astrometry, celestial mechanics, and geodesy including the solution of Kepler's equations of various kinds, the solution of the latitude equation, the Jacobian elliptic functions, the incomplete and complete elliptic integrals of all kinds, the associated Legendre functions of the first and second kind, the oblate spheroidal harmonics, and Lambert W-function.
Efficient numerical integration methods of orbital and rotational dynamics including the method of manifold correction, generalized Encke's method, Picard-Chebyshev method, super-implicit method, and various parallel computation techniques. Main Research Achievements T. Fukushima, e, "Numerical integration of gravitational field for general three-dimensional objects and its application to gravitational study of grand design spiral arm structure", MNRAS, , T.