A useful matrix form of Kane's equations (Q916436)

Recently there has been increasing interest in effective methods for obtaining dynamical equations of motion of large multibody systems. Besides the simplicity of the equations of motion to which a method leads and the amount of labor required for the formulation of the equations, an important criterion by which a method may be judged is the generality of the method, that is its validity for formulation of dynamical equations both in generalized coordinates and/or quasi-coordinates. The suitness of the governing equations produced for development of computer algorithms is also an important facet. One of the methods used widely in obtaining the dynamical equations of motion of large multibody systems, which has gained tremendous popularity in this decade, is the use of Kane's equations. In this note a matrix form of Kane's equations is presented. The formulation has been derived from d'Alambert's principle in the Lagrangian form, and was aimed at more clear and automatic (computer possibly) generation of the dynamical equations of motion of multibody systems, as compared with the original formulation.