  We investigate the consistency of the fundamental governing equations of
motion in continuum mechanics. In the first step, we examine the governing
equations for a system of particles, which can be considered as the discrete
analog of the continuum. Based on Newton's third law of action and reaction,
there are two vectorial governing equations of motion for a system of
particles, the force and moment equations. As is well known, these equations
provide the governing equations of motion for infinitesimal elements of matter
at each point, consisting of three force equations for translation, and three
moment equations for rotation. We also examine the character of other first and
second moment equations, which result in non-physical governing equations
violating Newton's third law of action and reaction. Finally, we derive the
consistent governing equations of motion in continuum mechanics within the
framework of couple stress theory. For completeness, the original couple stress
theory and its evolution toward consistent couple stress theory are presented
in true tensorial forms.
