Exploring Lagrangian and Hamiltonian Mechanics Through a Two-Degree-of-Freedom System: A Scaffolded Student Project Approach

Abstract

In this paper, we present a step-by-step description of a student project that illustrates the application of Lagrangian and Hamiltonian mechanics to a two-degree-of-freedom system. As part of the project, students explored both formalisms' peculiarities, identified conservation laws, and calculated integrals of motion. Students gained valuable experience by working with different approaches and observing the consistency with which they achieved equivalent results. The study has been fulfilled with a single cohort of fourteen undergraduate students. Each student received an individual version of the project with different initial conditions. Students uploaded the completed projects in a form of a brief report to a learning platform Moodle. The next stage was the teacher’s review of the project and its evaluation. An evaluation was conducted for each of the three parts of the project, described in detail in the paper. After that, an individual meeting was held with each student to clarify the evaluation result. As part of this meeting, the student was surveyed about what was the most difficult and whether the result matched the expectations. Analysis of the assessment data showed a 20% improvement in conceptual understanding and demonstrated that all students could successfully apply both Lagrangian and Hamiltonian approaches to the physical system being modelled.