Comment on 'Relationship between Kane's equations and the Gibbs-Appell equations'

Abstract

T^ESLOGE purports to show that equations are -LJsimply a of the Gibbs... equations.... Now, any valid method for .formulating dynamical equations can be shown to be intimately related to any other. Hence, it is a foregone conclusion that Kane's equations can be obtained with the aid of Newton's and that Gibbs' can be deducted from both; in fact, any one of these principles can be regarded, with equal justice, as a particular form of any of the others. Hence, this aspect of Desloge's Note has no merit. However, the Note can give rise to two questions of real substance, namely, do Kane's and Gibbs' methods differ from each other significantly, and which one is better suited for the actual formulating of equations of motion for complex multibody systems? An experienced dynamicist who has used both Kane's method and Gibbs' to formulate, in all detail, explicit dynamical equations for truly complex systems can answer both questions immediately: The two methods differ from each other significantly, and Kane's method is superior. Let us examine these claims briefly. The basis for Kane's method is his observation that, for a dynamical system S possessing n degrees of freedom, the inertial angular velocity o> of any rigid body belonging to S can always be expressed as