Nominal geometry and force measures for solids and fluids

Understanding solid- and fluid-inertia forces and their coupling with the gravity potential in complex motion scenarios is necessary for evaluating system stability and identifying root causes of system failure and accidents. Because solids and fluids have an infinite number of degrees of freedom and distributed inertia and elasticity, having meaningful qualitative and quantitative nominal measures of the kinematics and forces will contribute to a better understanding of the system dynamics. This paper proposes developing new continuum-based nominal measures for the characterization of the oscillations and forces. By using a material-point approach, these new nominal measures, which have their roots in the continuum-mechanics partial-differential equations of equilibrium and Frenet geometry, are independent of the formulation or generalized coordinates used to develop the dynamic equations of motion. The paper proposes a data-driven-science approach to define a nominal continuum space-curve geometry with nominal curvature and torsion; a nominal instantaneous motion plane (IMP), which contains the resultant of all forces including the inertia forces; and a nominal instantaneous zero-force axis (IZFA) along which the resultant of all forces vanishes. While using the material-point approach eliminates the need for introducing moment equations associated with orientation coordinates, the IMP and IZFA concepts can be used to define the instantaneous axis of significant moment components, which can lead to accidents such as in the case of vehicle rollovers.