MATHEMATICAL MODELING OF MECHANICAL SYSTEMS: FUNDAMENTAL PRINCIPLES AND METHODS

Аннотация

Mathematical modeling of mechanical systems is an essential process in engineering that enables the analysis, simulation, and design of real-world mechanical structures. This paper presents a comprehensive overview of the foundational principles and methods used in the modeling of mechanical systems. The discussion includes Newtonian and Lagrangian mechanics, differential equations, transfer functions, and state-space representations. Various types of mechanical systems— ranging from simple single-degree-of-freedom models to complex distributed parameter systems—are examined. Additionally, practical applications in automotive, aerospace, civil, and robotic engineering are highlighted. The paper also addresses the challenges associated with nonlinear behavior, parameter uncertainty, and model validation. By understanding and applying appropriate modeling techniques, engineers can enhance system performance, reliability, and safety in modern engineering design. Keywords: Mechanical systems, mathematical modeling, Newtonian mechanics, Lagrangian dynamics, differential equations, state-space representation, transfer functions, system dynamics, engineering applications, vibration analysis.