USING THE LAGRANGE EQUATION TO SOLVE MECHANICS PROBLEMS INVOLVING CONSTRAINTS AND SUPPORTS
Keywords:
Mechanics; equation of motion; Lagrangian function; Lagrange equation; generalized coordinate; principle of least action; action integral; partial derivative; constraint; reaction force.Abstract
This article examines the theoretical and practical aspects of solving mechanics problems involving constraints and supports using the Lagrange equation. Compared with traditional Newtonian methods, the approach based on the Lagrange formalism allows one to derive equations of motion, determine the reaction forces of constraints, and analyze representative systems such as the pendulum, half-Atwood machine, yo-yo, spherical surface, and inclined plane. The approach helps students develop theoretical thinking, a deeper understanding of mechanical phenomena, and the ability to solve problems by diverse analytical methods.
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