Analytical Mechanics

Analytical mechanics is a branch of physics that studies the motion of objects using mathematical formulations, rather than just forces and accelerations as in classical mechanics. It primarily includes Lagrangian mechanics, which focuses on energy and the principle of least action, and Hamiltonian mechanics, which relates to energy conservation and dynamical systems. These methods provide powerful tools for analyzing complex systems, making it easier to solve problems in mechanics, especially in systems with constraints or in different coordinate systems. This approach emphasizes elegance and efficiency in understanding motion.