The following equation of rolling motion is treated to study a capsizing condition. θ_a+2K_eθ_a+ω_0^^2f(θa)=(γπH/λ)ω^2 sin ωt where f(θ_a)=θ_a+β_3θ_a^^3+…+β_<2n+1> θ_a^<2n+1>, θa:apparent rolling angle, K_e:damping coefficient, ω_0:natural frequency, γ:coefficient of effective wave sloap, πH/λ:angle of maximum wave sloap, ω:wave frequency, t:time, and :differenciating with respect to t, β:non-linear factors and n:natural number. The swings capsizing from weather side to lee side are taken out. Under some assumptions, the most severe capsizing condition in these swings is approximately obtained as follows, [numerical formula] where [munerical formula] θ_υ:vanishing angle of stability, ν:ω/ω_0, A:(∣θ_<awm>∣+θ_υ)/2, and θ_<awm>:minimum heel angle in weather side to induce the capsizing. The relation between the ship stability and the capsizing is able to discuss by using critical lines calculated by the above equation. Results of the discussion are examined through numerical simulations and experiments used in three type models without shipping Water.
