Although it is known from previous studies that porpoising in high-speed planing craft is a Hopf bifurcation, this study examined its occurrence and disappearance using the motion model identified from full-scale test data. Herein, we first analyzed the stability of the system linearized near the equilibrium point. From its results, we reconfirmed the knowledge that porpoising occurs when the system becomes unstable in the vicinity of the equilibrium point. We also found that the system became unstable as the thrust or trim angle of the outboard motor decreased. This finding was consistent with the results of a full-scale craft test performed in a previous study. Second, we confirmed that the limit cycle which is a result of the nonlinearity of the system was stable. The two analyses indicate that porpoising corresponds to the supercritical Hopf bifurcation. Furthermore, in the vicinity of the bifurcation point, it was found that stable equilibrium points and stable limit cycles can coexist. Finally, we confirmed this phenomenon in the full-scale test.

尽管从之前的研究中知道高速滑行艇中的海豚运动是Hopf分岔，但本研究利用从全尺寸测试数据中确定的运动模型来检验其发生和消失。在这里，我们首先分析了平衡点附近线性化系统的稳定性。从其结果中，我们再次证实了当系统在平衡点附近变得不稳定时会发生海豚效应的知识。我们还发现，随着舷外发动机的推力或纵倾角减小，系统变得不稳定。这一发现与之前研究中进行的全面工艺测试的结果一致。其次，我们确认了由系统非线性引起的极限环是稳定的。两项分析表明海豚对应于超临界 Hopf 分岔。此外，在分岔点附近，发现稳定平衡点和稳定极限环可以共存。最终我们在全尺寸测试中证实了这一现象。