Analytical mechanics focuses on deriving equations of motion using principles such as Lagrangian and Hamiltonian mechanics, emphasizing energy and momentum conservation. In contrast, continuum mechanics studies the behavior of materials modeled as continuous mass rather than discrete particles, addressing stress, strain, and deformation. The two fields intersect, as analytical methods can be applied to solve problems in continuum mechanics. The discussion highlights the need for a more specific question to effectively address the differences. Understanding both areas is crucial for advanced studies in physics and engineering.