On Derivation of Motion Equations for Systems with Non-Holonomic High-Order Program Constraints

The paper develops and discusses the generalization of modeling methods for systems with non-holonomic constraints. The classification of constraints has been revisited and a concept of program constraints introduced. High-order non-holonomic constraints (HONC), as presented in examples, are the generalization of the constraint concept and may, as a constraint class, include many of motion requirements that are put upon mechanical systems. Generalized program motion equations (GPME) that have been derived in the paper can be applied to systems with HONC. Concepts of virtual displacements and a generalized variational principle for high-order constraints are presented. Classical modeling methods for non-holonomic systems based on Lagrange equations with multipliers, Maggi, Appell–Gibbs, Boltzman–Hamel, Chaplygin and others are peculiar cases of GPME. The theory has been illustrated with examples of high-order constraints. Motion equations have been derived for a system subjected to a constraint that programmed a trajectory curvature profile. Efficiency, advantages and disadvantages of GPME have been discussed.