In the past few decades, the electro-mechanical power-trains (EMPTs) are being used to replace the conventional power-trains in a few transportations, such as "More Electric Aircraft" and "Hybrid Electric Vehicle", to improve the energy efficiency and reduce greenhouse emissions. In the EMPTs, the electrical components such as electric machines, power electronics, controllers, and batteries are introduced. To accommodate these new components, the new power-train configurations are also involved. Due to the new components and new configurations, the application of the EMPTs gets a few challenges, including: (1) the nonlinear dynamics in the power-trains have not been sufficiently investigated, resulting in a limitation of the design optimization formulations that can reduce the vibration and noise levels in the power-trains; (2) the electro-mechanical interactions in an EMPT are not fully understood, especially the reflection of the vibration signature onto the stator current of electric machines. Therefore, the stator current has so far not been effectively utilized to analyze the dynamics and monitor the health of the EMPTs; and (3) modeling of the EMPTs is challenging and time consuming due to a large variation in the modeling strategies with respect to an EMPT's configuration and the intended research application. In other words, there is a lack of a modeling strategy that could be applicable to various types of the EMPTs and be implemented with relative ease. Subscript: pi represents the planet where i=1 to 4 s, a, and c represents the sun gear, annulus gear, and carrier
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