Abstract:

This paper reports on an innovative pedagogical intervention in a third-semester differential equations course for engineering students, aimed at strengthening their understanding of dynamical systems through the integration of Lagrangian–Hamiltonian modeling and MATLAB-based numerical simulation. The instructional sequence bridges traditional analytical solution techniques with energy-based modeling of mechanical systems.

The experience centers on a capstone project in which students, working in small teams, select a non-trivial mechanical system and perform a complete analytical derivation by defining generalized coordinates, formulating kinetic and potential energies, constructing the Lagrangian and Hamiltonian, and deriving the canonical equations of motion. These equations are then implemented in MATLAB using a fourth-order Runge–Kutta (RK4) method to simulate the system’s dynamics.

The project culminates in the production of an academic poster integrating analytical derivations, selected MATLAB code, numerical results, and dynamic visualizations, complemented by QR-linked animations. Student work was evaluated using analytical and communication rubrics and presented at a faculty-wide student research event.

Analysis of student artifacts and feedback indicates that this integrated approach enhances conceptual understanding of differential equations and theoretical mechanics, promotes student autonomy, and strengthens the ability to translate abstract mathematical models into executable simulations. The proposed framework offers a scalable and transferable model for enriching differential equations instruction in engineering education.

Keywords:

Higher Education, STEM Education, Numerical Simulation, Differential Equations.