Corrigendum: New Form of Kane’s Equations of Motion for Constrained Systems

A correction to the previously published article “New Form of Kane’s Equations of Motion for Constrained Systems”1 is presented. Misuse of the transformation matrix between time rates of change of the generalized coordinates and generalized speeds (sometimes called motion variables) resulted in a false conclusion concerning the symmetry of the generalized inertia matrix. The generalized inertia matrix (sometimes referred to as the mass matrix) is in fact symmetric and usually positive definite when one forms nonminimal Kane’s equations for holonomic or simple nonholonomic systems, systems subject to nonlinear nonholonomic constraints, and holonomic or simple nonholonomic systems subject to impulsive constraints according to Refs. 1, 2, and 3, respectively. The mass matrix is of course symmetric when one forms minimal equations for holonomic or simple nonholonomic systems using Kane’s method as set forth in Ref. 4. ∗Aerospace Engineer, Space Mission Analysis Branch, Mail Stop 462, E-mail: [email protected]. Senior Member, AIAA. †Assistant Professor, Aeronautical Engineering Department, E-mail: [email protected]. ‡Professor, School of Aerospace Engineering, E-mail: [email protected]. Fellow, AIAA. §Professor, George W. Woodruff School of Mechanical Engineering, E-mail: [email protected].