Mecánica clásica: Clase 1

Newton published his mathematical formulation of mechanics in the late 17th century, marking the beginning of mechanics as a scientific discipline and leading to the development of scientific thought.

Newton successfully resolved many problems that mathematicians and philosophers had been working on for the first time, leading to the formulation of theoretical frameworks and new ways of calculation that allowed solving problems Newton had not been able to.

Lagrange, a notable mathematician and physicist from Italy, introduced an extraordinary formulation in mechanics known as the Lagrangian formulation, which is the focus of discussion in the session.

Lagrangian equations offer practical advantages, such as the use of various coordinate systems like polar coordinates, which are not always obvious but provide benefits in terms of practical application and theoretical framework.

The Lagrangian equations can be derived from a variational principle, which may not seem obvious at first but serves as a foundational concept in physics and general science theories, leading to a deeper understanding of dynamics and particle movement.

The discussion extends to the use of generalized coordinates in Lagrangian equations, accounting for different coordinate systems beyond Cartesian coordinates and emphasizing the flexibility and applicability of Lagrangian dynamics in various scenarios.

Exploration of diverse coordinate systems and constraints in Lagrangian mechanics, enabling a deeper understanding of complex physical problems by considering specific limitations and relationships within the system.

Se plantean y se resuelven las ecuaciones radial y angular en el contexto de un problema físico.

Se calculan las derivadas de Ldr y de R punto en el contexto de la fuerza Schubert y la aceleración.

Se discute la relación entre el momento angular, la inercia de la partícula y la ecuación del momento angular.

Se plantea un ejemplo más sofisticado con el péndulo plano y se elige un sistema de coordenadas generalizadas.

Se analiza un sistema con un resorte de constante y se eligen coordenadas generalizadas para expresar la energía cinética y potencial.

Se describe un ejemplo de la máquina de Atwood con dos masas distintas y se plantea un vínculo entre las coordenadas.