$235$ What are some theoretical foundations in mechanical engineering that serve as cornerstones for understanding the principles and applications of mechanical systems? Explore key concepts such as thermodynamics, fluid mechanics, solid mechanics, dynamics, materials science, and control theory, elucidating their roles in designing, analyzing, and optimizing mechanical systems. How do these theoretical frameworks underpin various engineering disciplines, ranging from aerospace to automotive engineering, and how do they contribute to innovations in fields like robotics, renewable energy, and manufacturing processes?