Abstract
This article examines a drill string modeled as a long elastic rod connecting the bit and surface equipment. The drill string is considered the primary element of a drilling dynamic system (DDS). A dynamic model is created, and equations for the DDS’s longitudinal oscillations are derived. A method for solving wave equations and longitudinal oscillation equations is developed, enabling the analysis of the stressstrain state of drill strings. Stresses at the string attachment points to surface equipment are calculated. The feasibility of using variational principles of mechanics to study nonlinear longitudinal oscillations of a heavy drill string with lumped parameters is established. The results of the study contribute to improving the quality of applied analysis in scientific work.