ABSTRACT
As stated throughout this book, the development of (correct) governing equations of motion for systems of particles or rigid bodies is the central task of dynamics.
Newton’s third law of motion for particles ∑ =f mr (or its extension to planar motion of rigid bodies) has been the basis for deriving most of the equations of motion. For multi-degree-of-freedom (MDOF) problems, these developments have proceeded from a freebody diagram using force and moment equations. For one-degree-of-freedom (1DOF) examples, parallel developments using Newtonian and work-energy approaches have applied. For 1DOF models, starting with the work-energy equation Workn.c. = Δ(T + V) and differentiating this equation with respect to the displacement or rotation coordinate yielded the equation of motion without recourse to a free-body diagram. Moreover, with this approach, the kinematics development was simpler because only velocities are required to define the kinetic energy versus accelerations when applying ∑ =f mr. Recall thatthe advantages of an energy-based approach diminish when energy dissipation is present.
