A New Formulation of the Equations of Dynamics

In a recent paper 1] the author introduced a new method for handling differentials and extrema in the presence of constraints, in which the constraints were represented by a projection matrix. For extrema this method can be used instead of Lagrange multipliers. Here the same idea is applied to the equations of motion in mechanics, leading to a new formulation in both Cartesian and generalized coordinates, equivalent to Lagrange's equations and applicable with both holonomic and nonholonomic constraints. The present formulation provides an alternative to a recent approach of Kalaba, Udwadia, and Xu 2,3], which too is based on linear algebra, and to Appell's classical method for the nonholonomic case