Shortcomings in T. R. Kane’s paper [J. Appl. Mech. 28, 574-578 (1961)] are discussed in the first section. Kane’s equation is derived in this paper directly from first principles in analytical dynamics, namely from the d’Alembert-Lagrange equation, and the necessity as well as the sufficiency of the equation is proved.
The author suggests that Kane’s equation may be called generalized d’Alembert equation in quasi-coordinates, and shows that it is equivalent to Appell’s equation through a given relation. ”Power formulas” for the given force system and for the inertial force system are given. An extended Kane’s equation for a nonlinear nonholonomic system of first order is derived from Gauss’ principle.