Analytical mechanics is a branch of theoretical physics that reformulates classical mechanics to provide deeper insights into physical systems. It emphasizes the use of mathematical principles, such as Lagrangian and Hamiltonian mechanics, to analyze motion and forces. Unlike Newtonian mechanics, which relies on vector quantities like force and acceleration, analytical mechanics utilizes scalar functions, offering a more generalized framework. It is particularly powerful in dealing with systems with constraints or complex geometries. Widely used in fields like celestial mechanics, quantum mechanics, and engineering, it bridges classical and modern physics, enhancing our ability to model and predict physical phenomena efficiently.