This paper provides a complete analytical evalua-tion of the energy derivatives governing variable-mass systems,specifically examining the Kh-47M2 Kinzhal hypersonic missile.We investigate the mechanical implications of higher-order kine-matic terms, such as jerk, coupled with mass flux variables.Furthermore, we simulate a three-stage orbital directed-energyengagement mechanism operating at high altitudes, detailing theexplicit differential equations governing the thermal responseof the titanium alloy casing alongside the control loop degra-dation that induces subsequent aerodynamic breakup duringatmospheric re-entry.