Junyan Xu

Li Xie, Yiqun Zhang, Junyan Xu

In the first part of this paper, inspired by the geometric method of Jean-Pierre Marec, we consider the two-impulse Hohmann transfer problem between two coplanar circular orbits as a constrained nonlinear programming problem. By using the Kuhn-Tucker theorem, we analytically prove the global optimality of the Hohmann transfer. Two sets of feasible solutions are found, one of which corresponding to the Hohmann transfer is the global minimum, and the other is a local minimum. In the second part, we formulate the Hohmann transfer problem as two-point and multi-point boundary-value problems by using the calculus of variations. With the help of the Matlab solver bvp4c, two numerical examples are solved successfully, which verifies that the Hohmann transfer is indeed the solution of these boundary-value problems. Via static and dynamic constrained optimization, the solution to the orbit transfer problem proposed by W. Hohmann ninety-two years ago and its global optimality are re-discovered.

Jianxing Liao, Junyan Xu, Yatao Sun et al.

Designing complex computer-aided design (CAD) models is often time-consuming due to challenges such as computational inefficiency and the difficulty of generating precise models. We propose a novel language-guided framework for industrial design automation to address these issues, integrating large language models (LLMs) with computer-automated design (CAutoD).Through this framework, CAD models are automatically generated from parameters and appearance descriptions, supporting the automation of design tasks during the detailed CAD design phase. Our approach introduces three key innovations: (1) a semi-automated data annotation pipeline that leverages LLMs and vision-language large models (VLLMs) to generate high-quality parameters and appearance descriptions; (2) a Transformer-based CAD generator (TCADGen) that predicts modeling sequences via dual-channel feature aggregation; (3) an enhanced CAD modeling generation model, called CADLLM, that is designed to refine the generated sequences by incorporating the confidence scores from TCADGen. Experimental results demonstrate that the proposed approach outperforms traditional methods in both accuracy and efficiency, providing a powerful tool for automating industrial workflows and generating complex CAD models from textual prompts. The code is available at https://jianxliao.github.io/cadllm-page/

Li Xie, Yiqun Zhang, Junyan Xu

We consider optimal two-impulse space interception problems with multi-constraints. The multi-constraints are imposed on the terminal position of an interceptor, impulse and impact instants, and the component-wise magnitudes of velocity impulses. We formulate these optimization problems as multi-point boundary value problems and the calculus of variations is used to solve them. All inequality constraints are converted into equality constraints by using slackness variable methods in order to use Lagrange multiplier method. A new dynamic slackness variable method is presented. As a result, an indirect optimization method is established for two-impulse space interception problems with multi-constraints. Subsequently, our method is used to solve the two-impulse space interception problems of free-flight ballistic missiles. A number of conclusions have been established based on highly accurate numerical solutions. Specifically, by numerical examples, we show that when time and velocity impulse constraints are imposed, optimal two-impulse solutions may occur, and also if two impulse instants are free, then two-impulse space interception problems with velocity impulse constraints may degenerate to the one-impulse case.