subroutine kvtx_fixed_lifetime(ktrk, update_track, vtx0,
     *                               ctau, sig_ctau, chisq, error)
*
* begin_doc
*
*  Given a track and a fixed starting point, calculate the c*tau
*  (tau = proper time) of the particle and its error.
*
*  Note: If the track is not updated here, you can update it later by
*  calling kfit_update_tracks.
*
*  Input Parameters:
*  ktrk          integer variable
*                Track number to fit
*
*  update_track  integer variable
*                 0 ==> Calculate chisquare only (do not update track)
*                 1 ==> Calculate chisquare, update track
*                 2 ==> Calculate chisquare, update track & cov matrix
*
*  vtx0(3)       double precision array
*                Starting point of particle
*
*  Output Parameters:
*  ctau          double precision variable
*                c*tau of the particle
*
*  sig_ctau      double precision variable
*                Error on ctau
*
*  chisq         double precision variable
*                Chisquare of fit
*
*  error         integer variable
*                 0 ==> All OK
*                >0 ==> Error
*
*  Other routines:
*
*  Notes:
*
*  >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
*   The constraint is imposed by the method of Lagrange multipliers.
*
*   I use the three equations of motion as the constraint equations from
*   which one unknown, ctau, must be determined, giving 2 degrees of
*   freedom. The 4x4 covariance matrix of (z,ctau) is stored, with the
*   lower 3x3 part set to zero.
*  >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
*
*  Author:   Paul Avery      Created:  Fri Aug 29 16:12:52 EDT 1997
*
*  Major revisions:
*
*
* end_doc