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The canonical generalized inversion dynamical equations of motion for ideally constrained discrete mechanical systems are introduced in the framework of Kane’s method. The canonical equations of motion employ the acceleration form of constraints and the Moore-Penrose generalized inversion based Greville formula for general solutions of linear systems of algebraic equations. Moreover, the canonical equations of motion are explicit and nonminimal (full order) in generalized accelerations, and their derivation is made without appealing to the principle of virtual work or to Lagrange multipliers. The geometry of constrained motion is revealed by the canonical equations of motion in an explicit and clear manner by partitioning the canonical generalized acceleration vector into two potions: a portion that drives the mechanical system to abide by the constraints,and a portion that generates the momentum balance dynamics of the mechanical system. Geometric interpretation of the equations is provided, which leads to verifying the Gauss’ principle of least constraints and its Udwadia-Kalaba interpretation.

Canonical Generalized Inversion Form of Kane’s Equations of Motion for Constrained Mechanical Systems