We give some deformations of the Rikitake two-disk dynamo system. Particularly, we consider an integrable deformation of an integrable version of the Rikitake system. The deformed system is a three-dimensional Hamilton-Poisson system. We present two Lie-Poisson structures and also symplectic realizations. Furthermore, we give a prequantization result of one of the Poisson manifold. We study the stability of the equilibrium states and we prove the existence of periodic orbits. We analyze some properties of the energy-Casimir mapping \(\cal{E}\cal{C}\) associated to our system. In many cases the dynamical behavior of such systems is related with some geometric properties of the image of the energy-Casimir mapping. These connections were observed in the cases when the image of \(\cal{E}\cal{C}\) is a convex proper subset of ℝ². In order to point out new connections, we choose deformation functions such that \(\rm{IM}\cal{E}\cal{C}=\mathbb{R}^{2}\). Using the images of the equilibrium states through the energy-Casimir mapping we give parametric equations of some special orbits, namely heteroclinic orbits, split-heteroclinic orbits, and split-homoclinic orbits. Finally, we implement the mid-point rule to perform some numerical integrations of the considered system.

我们给出了Rikitake两盘式发电机系统的一些变形。特别是，我们考虑了Rikitake系统的可积分版本的可积分变形。变形系统是三维汉密尔顿-泊松系统。我们介绍了两个李泊松结构以及辛实现。此外，我们给出了泊松流形之一的预量化结果。我们研究了平衡态的稳定性，并证明了周期轨道的存在。我们分析了与系统关联的能量-卡西米尔映射\（\ cal {E} \ cal {C} \）的某些属性。在许多情况下，此类系统的动态行为与能量-卡西米尔映射的图像的某些几何特性有关。在\（\ cal {E} \ cal {C} \）的图像中观察到这些连接是ℝ的凸适当子集²。为了指出新的连接，我们选择变形函数，例如\（\ rm {IM} \ cal {E} \ cal {C} = \ mathbb {R} ^ {2} \）。使用通过能量-卡西米尔映射的平衡态图像，我们给出了一些特殊轨道的参数方程，即异斜轨道，分裂异斜轨道和分裂同斜轨道。最后，我们执行中点规则以对所考虑的系统进行一些数值积分。