Teaching mechanics: Between rigor, applications, and misconceptions

This paper examines the role of rational mechanics in modern engineering education, arguing that its marginalization in contemporary curricula represents a significant pedagogical limitation. Although mechanics is often first encountered by engineering students in introductory physics courses and later developed in applied engineering subjects, these approaches frequently emphasize problem-solving techniques and phenomenological descriptions rather than conceptual clarity and theoretical coherence. Drawing on historical and epistemological perspectives and a critical analysis of widely used teaching materials, we highlight the distinctive nature of rational mechanics as a mathematical science grounded in experience and developed through rigorous abstraction.We show that the presentation of fundamental concepts in standard physics textbooks may lead to conceptual imprecision and fragmentation, limiting a deeper understanding of the principles underlying engineering applications. A comparison with applied mechanics further suggests that, without a solid grounding in rational mechanics, mechanical knowledge risks becoming a collection of specialized methods rather than a coherent theoretical framework. By contrast, rational mechanics provides an “economy of thought” that unifies mechanical principles, supports the interpretation of physical phenomena, and promotes mathematical modelling in engineering.We conclude that reintegrating rational mechanics into engineering curricula would strengthen students' ability to connect theory and practice while developing transferable analytical modelling skills. Rather than an obsolete discipline, rational mechanics should be regarded as a foundational component of engineering education. This paper clarifies its educational role relative to introductory physics and applied mechanics and presents a historically and epistemologically grounded argument for its reintegration into modern engineering curricula.