A Reviewed Version of Lagrangian Mechanics: An Introduction of Citician Dynamics in Classical Mechanics

Citician is an advanced concept in classical dynamics, serving as a reviewed version of the Lagrangian formalism. It is defined as the total time derivative of a system's Lagrangian. While its functional structure mirrors that of the Lagrangian, the behavior of the Citician aligns more closely with the Hamiltonian. Fundamentally, Citician represents twice the instantaneous power of a holonomic system where the Lagrangian is not an explicit function of time. A defining feature of Citician is its dependence on both the first and second derivatives of generalized coordinates, despite having only a single independent variable, similar to the Lagrangian. This dependency leads to deriving three canonical equations using conjugate coordinates (q, p) within phase space. In this regard, Citician's action parallels that of the Hamiltonian while offering a broader spectrum of transformations, making it particularly valuable for simplifying complex solutions. Citician mechanics is characterized by its succinctness and adaptability, especially in moving or disconnecting fluid boundaries. It applies to simple systems such as a bouncing ball, pendulum, or oscillating spring—where energy oscillates between kinetic and potential forms. However, its true strength lies in modeling more intricate dynamic systems, such as planetary orbits in celestial mechanics.