Abstract: Thermal hydraulic problems under motion conditions are usually studied in non-inertial reference frames for convenience, which results in the necessity of gravity vector transformation and additional forces calculation. Based on the strict mathematical deductions, the transformation matrix of orthogonal coordinates for 3 dimensional rotating has been derived and the general expression for liquid force per unit mass under non-inertial reference frame was obtained in this paper. Forces under various typical ocean moving conditions were also calculated and discussed for application purpose. This paper provides a useful reference for thermal hydraulic researches under motion conditions.