The generalized Hamiltonian function is proposed for the brushless DC motor (BLDCM) chaotic system. The Hamiltonian and Casimir functions are derived from the generalized Hamiltonian function. In this way the Casimir energy is proven to be a special type of the generalized Hamiltonian function. The derivative of the Hamiltonian function is used for analyzing the various dynamical behaviors under different combination of energy components. An analytical optimal bound of the BLDCM is simply proposed from the Hamiltonian power. Along the study, the comparison between the Hamiltonian and Casimir powers is conducted, and physical interpretations and mechanism revealing the onset of chaos are provided for the BLDCM chaotic system. Bifurcation analysis through the Hamiltonian power and Casimir power identifies the different dynamic patterns.

中文翻译：

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基于哈密顿量的无刷直流电机混沌系统能量分析

针对无刷直流电机（BLDCM）混沌系统提出了广义哈密顿函数。哈密​​顿函数和卡西米尔函数派生自广义哈密顿函数。这样就证明了卡西米尔能量是广义哈密顿函数的一种特殊类型。哈密​​顿函数的导数用于分析不同能量成分组合下的各种动力学行为。简单地从哈密顿幂提出了 BLDCM 的解析最优界限。在研究过程中，对哈密顿幂和卡西米尔幂进行了比较，为BLDCM混沌系统提供了揭示混沌发生的物理解释和机制。通过哈密顿幂和卡西米尔幂的分岔分析确定了不同的动态模式。