Application of Frequency Regulation in Newtonian Mechanical Systems

This report formalizes a mathematical model for controlling the operational frequency of high-load mechanical transmission systems (gears and chains) based on Newtonian principles. Unlike detonation-driven systems, this model focuses on kinetic energy dissipation through frictional torque. In Newtonian mechanics, the work done by friction in rotational motion is converted into heat. The mechanical power loss in a gear mesh or chain link is defined by the product of frictional torque and angular velocity : P(loss) = (N ⋅ m) loss × ω f target ≈ ( (N ⋅ m)loss ⋅ ω )/(m ⋅ cp ⋅ ΔT allowable )