On the structure of linear, first-order nonholonomic constraints, and the associated reaction forces

This paper reexamines: (i) the analytical and physical structure of (linear, first-order) nonholonomic constraints and their associated reaction forces, and (ii) the effect of the motion of the frame of reference on the forms of these constraints and forces, in parallel with the constitutive equation theory of continuum mechanics; all the results are expressed in both particle (vectorial) and system forms. The theory clearly shows the precise way in which the acatastatic terms (in the system form of the nonholonomic constraints and in inertial system coordinates) are generated by the motion of the frame of reference relative to inertial space. The general theory is finally applied to the well-known knife-edge/sled problem in a uniformly rotating frame of reference.