Hamiltonian Analysis of Charged Particle Gyromotion in Cylindrical Coordinates

: A Hamiltonian approach in cylindrical coordinates is applied to the motion of charged particles in a uniform axial magnetic field. The method is compared to the traditional approaches of uniform circular motion and Newtonian mechanics. Cylindrial coordinates are preferred in many practical situations such as application to laboratory experiments. The advantage cylindrical coordinates offer is the ability to form a one-dimensional effective potential, which can be used to determine a number of spatial and temporal characteristics of the resulting cyclotron motion without an explicit solution of the equations of motion. This approach provides a different perspective into the dynamics of Larmor motion to complement the traditional approaches.