swift/orbel/orbel_zget.f

***********************************************************************
c                    ORBEL_ZGET.F
***********************************************************************
*     PURPOSE:  Solves the equivalent of Kepler's eqn. for a parabola 
*          given Q (Fitz. notation.)
*
*             Input:
*                           q ==>  parabola mean anomaly. (real scalar)
*             Returns:
*                  orbel_zget ==>  eccentric anomaly. (real scalar)
*
*     ALGORITHM: p. 70-72 of Fitzpatrick's book "Princ. of Cel. Mech."
*     REMARKS: For a parabola we can solve analytically.
*     AUTHOR: M. Duncan 
*     DATE WRITTEN: May 11, 1992.
*     REVISIONS: May 27 - corrected it for negative Q and use power
*	      series for small Q.
***********************************************************************

	real*8 function orbel_zget(q)

      include '../swift.inc'

c...  Inputs Only: 
	real*8 q

c...  Internals:
	integer iflag
	real*8 x,tmp

c----
c...  Executable code 

	iflag = 0
	if(q.lt.0.d0) then
	  iflag = 1
	  q = -q
	endif

	if (q.lt.1.d-3) then
	   orbel_zget = q*(1.d0 - (q*q/3.d0)*(1.d0 -q*q))
	else
	   x = 0.5d0*(3.d0*q + sqrt(9.d0*(q**2) +4.d0))
	   tmp = x**(1.d0/3.d0)
	   orbel_zget = tmp - 1.d0/tmp
	endif

	if(iflag .eq.1) then
           orbel_zget = -orbel_zget
	   q = -q
	endif
	
	return
	end    ! orbel_zget
c----------------------------------------------------------------------