Discrete models of two drilling stabilizer designs are subject to analytical mechanics treatments to examine dynamic behavior and amplify insights into contribution to bottom-hole drilling assembly (BHA) dynamics stability. The spiral blade and straight blade design stabilizers are essential components of oil and gas BHA included to functionally provide stabilization during rotation of the BHA and stand-off from the walls of the oil and gas wellbore. Attempts are made from the onset to simplify model complexity and as a consequence ease of computational simulation. The answer to the seemingly intuitive question of the mechanical advantage offered by a spiral blade compared to a straight blade stabilizer design in a constrained dynamics representation is revealed by computing forces generated at the interface between the functional elements of the devices and the inelastic boundary (wellbore) to keep the constraint satisfied. Analytical mechanics approaches have been used to carry out 3-D dynamics analysis of bottom hole drilling assemblies using 3-D Euler-Bernoulli or Timoshenko beam-column finite-element representations and lumped-parameter model approximations of rigid body dynamics behavior. In this work, phase portraits of angular velocity versus displacement — parsed for torque generated — from numerical simulations for torque-free and applied external load states, and discussion, offer illuminating insights into downhole operating dynamics of these ubiquitous components of oil and gas well bottom hole assembly (BHA) drilling devices.