Generalized Panofsky-Wenzel theorem in curvilinear coordinate systems applicable to non-ultrarelativistic beams

This note gives an introduction to the theories of impedances and wakes in particle accelerators. The standard formulation assumes that the beam is traveling along a straight orbit with constant velocity $\vec{v}=v{\vec{e}}_z$. On this note, we show the possibility of extending the formulation for beams traveling along a curved orbit but assuming $\mathrm{\mid }\vec{v}\mathrm{\mid }=v$ to be constant.