Routhian mechanics

Routhian mechanics is a formulation in physics that simplifies analyzing systems with many moving parts, especially when some variables are easier to handle than others. It combines aspects of Lagrangian and Hamiltonian mechanics by transforming the equations to focus on selected variables, called generalized coordinates and their conjugate momenta, while reducing the complexity of the problem. This approach is particularly helpful when certain degrees of freedom are cyclic (do not change over time), allowing for easier calculation of motion. Essentially, Routhian mechanics provides a streamlined way to understand the dynamics of complex systems by re-expressing their energy-like functions to facilitate solving their equations of motion.