Kane's equations or Jourdain's principle?

摘要

This paper discusses the relationships between Kane's equations and Jourdain's principle. In 1961 Kane published a paper: "Dynamics of Nonholonomic Systems". The method detailed in that paper, since named Kane's equations, has been popular in the modelling of mechanical systems especially in robotics. It was often stated that Kane's equations were a novel way of modelling. However, in 1909, Jourdain published a paper titled "Note on an analogue of Gauss' principle of least constraint" where he established the principle of virtual power that is equivalent to Kane's equations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>