Analytical mechanics is a branch of physics that focuses on the principles of motion and forces using mathematical formulations. It provides a framework for understanding how objects move and interact, often employing concepts like energy and momentum. This approach is particularly useful for solving complex problems in mechanics that may be difficult to analyze using traditional methods. The two main formulations of analytical mechanics are Lagrangian mechanics and Hamiltonian mechanics. Both methods use different mathematical techniques to derive equations of motion, making it easier to study systems with multiple interacting parts. These formulations are widely used in fields such as classical mechanics, quantum mechanics, and astrophysics.