Lecture
This lecture covers fundamental concepts in continuum mechanics, focusing on Newton's third law and the symmetry of the stress tensor. It begins by discussing how forces are transmitted in continua and the importance of understanding the geometry of a body's motion. The instructor explains the governing equations of continuum mechanics, including mass conservation and energy conservation principles. The lecture also delves into the mathematical tools necessary for expressing theories and solving problems, such as tensor calculus and dimensional analysis. The significance of linear momentum balance and angular momentum balance is highlighted, along with the evaluation of divergence in stress tensors. The lecture concludes with a discussion on the implications of these principles in the context of fluid motion and solid mechanics, emphasizing the role of constitutive laws in describing material behavior under deformation. Overall, this lecture provides a comprehensive overview of the foundational principles that govern the behavior of materials in continuum mechanics.