A geometric derivation of Kane's equationsA geometrically-based derivation of Kane's dynamical equations is presented. Equations for both holonomic and nonholonomic systems are derived by considering the system's motion in a hypersurface determined from the equations relating Cartesian to generalized coordinates. Using vector space methods, the equations of motion are projected onto the tangent plane to the hypersurface. In the course of this construction, a requirement on the transformation between generalized and Cartesian coordinates is revealed that is often overlooked. This restriction is then shown to be a necessary and sufficient condition for the invertibility of the coefficient matrix of the generalized accelerations appearing in Kane's dynamical equations. Although less succinct than the traditional approach, the present derivation offers some insight into the physics embodied in Kane's equations and appears as a natural generalization of methods used in elementary problems.
Document ID
19890043414
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Storch, Joel (California Institute of Technology Jet Propulsion Laboratory, Pasadena, United States)
Gates, Stephen (Charles Stark Draper Laboratory, Inc. Cambridge, MA, United States)
Date Acquired
August 14, 2013
Publication Date
January 1, 1989
Subject Category
Physics (General)
Report/Patent Number
AIAA PAPER 89-1305
Meeting Information
Meeting: AIAA, ASME, ASCE, AHS, and ASC, Structures, Structural Dynamics and Materials Conference