# Electrical Circuits Simulator in Null-Flux Electrodynamic Suspension Analysis
## 2 Unveiling the Inner Workings: Exploring the Principles and Model of an EDS System
### The Research Gap  
EDS is studied and examined using a variety of techniques and frameworks. These techniques give researchers a variety of instruments and approaches to research and examine EDS systems, each having its benefits and considerations, depending on the particular goals and complexities of the system under study. Analytical models based on theoretical concepts, such as electromagnetic theory and mechanical dynamics, are created to research particular facets of EDS. For better system performance and to acquire insights into system behavior, these models frequently simplify mathematical equations and presumptions. Physical models in scientific research often need more than oversimplification. As more details and complexities of the natural world are incorporated into these models, their resolution and analytical solvability become increasingly difficult. This phenomenon is commonly called the \"spherical cow of physics.\" It represents the trade-off between model simplicity and capturing the intricacies of reality. Researchers can make the systems more manageable and derive analytical solutions by assuming simplified shapes or disregarding certain complexities. However, it is crucial to recognize that such models may only partially capture the richness of real-world phenomena. Despite their limitations, physical models are valuable tools for gaining insights and understanding complex systems within the constraints of available resources and computational capabilities. They provide a foundation for further refinement, experimental validation, and the development of more comprehensive models in the pursuit of scientific knowledge. A numerical method known as the finite elements method (FEM) approximates the behavior within each part of a system to tackle complicated engineering issues. In EDS systems, the FEM is frequently used to thoroughly examine electromagnetic fields, forces, and material characteristics. While advantageous in its ability to create detailed and accurate models, it is burdened by the drawback of increased computational time and resource requirements. This disadvantage stems from the necessity to compute the physical equations within each small mesh domain, which demands significant computational effort. However, the method excels in its capacity to generate a model that closely approximates the behavior of an original system, allowing for more comprehensive understanding of the complex dynamics of the system. Despite its computational challenges, the FEM remains valuable in conducting in-depth analyses and simulations of various physical phenomena. The EDS system is effectively represented by applying DCT, which treats it as an electrical circuit comprising lumped parameters. This modeling approach considers various circuit characteristics that vary over time and space, governed by differential equations. As a result, it enables the dynamic and transient analysis of the system, ensuring precise force calculations and accommodating considerations of edge and end effects. Moreover, this methodology is rooted in the concept that the EDS system can be effectively simulated using an electrical circuit simulator. This topic is further elaborated upon in subsequent sections of this study. Numerical methods are used to determine the behavior of several systems under various operating conditions. In this study, these methods are employed to solve mathematical equations iteratively. Specifically, the numerical method calculates the derivatives of mutual inductances between the onboard and guide coils. For this purpose, the centered derivative method is employed, which relies on determining the slope between two neighboring points around the desired evaluation point. It is important to note that numerical calculations inherently introduce some errors. Thus, meticulous care must be taken to select the most suitable method for the specific problem, with the aim of leveraging the significant advantage of fast processing speed offered by numerical calculations.