Development of a platform for automated equation derivation and response analysis using images and text data of dynamic systems
摘要
This study proposes an innovative and practical platform aimed at transforming the paradigm of mechanical engineering education by integrating image-based dynamic system analysis with Lagrangian mechanics. Unlike conventional approaches that require manual derivation of equations, the proposed platform automates the process by leveraging image processing and computer vision technologies to automatically extract kinetic energy, potential energy, and constraint equations from images of mechanical systems. Based on these extractions, the platform utilizes Lagrangian mechanics to derive the system’s equations of motion. Additionally, high-precision numerical analysis is employed to compute and visualize the dynamic responses of the system, facilitating students’ intuitive understanding of system behavior. To validate the accuracy and reliability of the proposed method, numerical results are compared against example problems and solutions presented in various textbooks and educational resources, confirming the appropriateness of the computed responses. Implementing Python and GNU Octave, the platform is capable of learning from image data of various mechanical systems and automatically identifying and analyzing new images. This approach enables students to apply theoretical knowledge to real systems and to intuitively grasp the behavior of complex dynamic systems, thereby maximizing the effectiveness of their learning.