## 1 Introduction  
Linear induction motors (LIMs) have been applied to high-speed large-thrust electromagnetic (EM) propulsion applications, such as EM launch [1] and transportation systems [2]. Nevertheless, when the power is increased beyond a certain point, certain detrimental characteristics of LIMs, especially the power factor, are magnified [3]. Meanwhile, as the speed increases, the burden on the power supply system also increases, and the frequency of power electronic devices consequently limits the supply frequency and restricts the acceleration [4]. To balance the heavy burden on supply devices with the growing kinetic requirements, a variable pole pitch (VPP) EM propulsion scheme was proposed in [5, 6] and a VPP EM system propelled by a flat-secondary LIM was analyzed. However, when the challenges with typical LIMs are considered, such as low power factor, it is clear that previous VPP EM propulsion techniques suffer from poor performance as the input power increases [7]. To address those problems, we propose a VPP EM propulsion scheme using ladder-slot-secondary double-sided linear induction motors (LS-secondary DLIMs). LS-secondary DLIMs are capable of enhancing the power factor, which can be calculated via the finite element method (FEM) in [8]. However, this approach is commonly considered to be a method of verifying the characteristics of a previously designed machine, instead of being a general method to design and analyze new machines. In addition, the derivation of the EM field in the motor leads to an accurate but complex model [9, 10, 11]. Squirrel-cage rotary induction motors (RIMs) have been extensively studied, and mathematical models, analytical design methods [12], and equivalent circuit analyses are readily available [13]. However, because of the end effect in DLIMs [14], the mathematical model developed for RIMs cannot be used. In the absence of general methods to design, analyze and optimize LS-secondary DLIMs in practical scenarios, it is extremely difficult to successfully implement a VPP EM propulsion scheme due to the complexity of the model and the enormity of calculations. To accomplish our objective of designing a VPP EM propulsion scheme, we first present a generic method for designing an LS-secondary DLIM. In this paper, we propose a novel scheme for EM propulsion, i.e., the VPP EM propulsion using LS-secondary DLIMs, aiming at optimizing kinetic performance and enhancing machine characteristics simultaneously. A numerical analysis method is established based on equivalent circuit considering end effect of LS-secondary DLIMs. Due to applicability and generality of the equivalent circuit, the numerical analysis is a general method to design, estimate, and optimize the VPP EM propulsion using LS-secondary DLIMs. Consequently, this paper accomplishes the theoretical analysis of this novel EM propulsion scheme. This method is not only an effective and accurate method to estimate the performance of the novel configuration, but also utilization of LS-secondary DLIMs in the VPP EM propulsion may serve as a promising solution to high-speed large-thrust applications such as EM launch. This paper is organized as follows. Section 2 presents an equivalent circuit model based on [PERSON]'s model [15] for a single LS-secondary DLIM. Meanwhile, referring to the EM field in our previous work [16], stress analysis is carried out to determine whether designed LS-secondary DLIMs are feasible in practical scenarios. Section 3 first establishes the VPP EM propulsion scheme using LS-secondary DLIMs. Theory of numerical analysis for this scheme is then proposed. Kinetic characteristics, such as the acceleration of each sectional motor, the overall displacement, and the performance period, are analyzed with the aid of the equivalent circuit-based model of the LS-secondary DLIM.