On the use of quasi-velocities in impulsive motion

Abstract The differential variational principle of Jourdain (JVP) is extended to cover the dynamics of impulsive motion, formulated in terms of quasi-velocities, instead of time rates of change of true or Lagrangian generalized coordinates. This enlarges the scope of the JVP, because the extension of its range to encompass the use of quasi-velocities (which includes true velocities as a special case), enables the analyst to solve a wider range of problems. It should be pointed out that the mathematical foundation of the JVP, which is based on the assumption that the variation of the position vectors as well as the time is zero (in true Lagrangian as well as quasi-coordinates), is ideally suited to the physics of impulsive motion, where finite changes in the velocity are accompanied by negligible changes in configuration and time.