.MCAD 301010000 1 74
.CMD PLOTFORMAT
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 15
.CMD FORMAT  rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge
.CMD SET ORIGIN 0
.CMD SET TOL 0.001000000000000
.CMD SET PRNCOLWIDTH 8
.CMD SET PRNPRECISION 4
.CMD PRINT_SETUP 1.200000 0
.CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables
.CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants
.CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text
.CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1
.CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2
.CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3
.CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4
.CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5
.CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6
.CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7
.CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=2 family=Arial points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=14 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0
.CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0
.CMD UNITS U=1
.TXT 3 1 0 0
Cg a73.000000,73.000000,126
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs28 \ul Acceleration in One
 Dimension}{ }{\f0 \fs16 by P. Fraundorf
 Copyright 1992-1995 @newton.umsl.edu: 11
 Oct 1995.}}
}
.TXT 3 0 0 0
Cg a66.125000,70.000000,96
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {First, some constants that are 
useful should you decide to change units
 in the calculation...}}
}
.TXT 3 0 0 0
Cg a10.125000,72.000000,18
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {speed of light:}}
}
.EQN 0 11 0 0
c:3*(10)^(8)*(m)/(sec)
.EQN 0 12 0 0
ly:c*yr
.EQN 0 8 0 0
ly=?m
.EQN 0 16 0 0
g=?(m)/((sec)^(2))
.EQN 0 13 0 0
g=?(ly)/((yr)^(2))
.TXT 5 -60 0 0
Cg a9.250000,58.000000,18
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {inertial units:}}
}
.EQN 0 10 0 0
iyr:1*yr
.EQN 0 10 0 0
c:1*(ly)/(yr)
.TXT 0 13 0 0
Cg a9.625000,28.000000,18
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {traveler units:}}
}
.EQN 0 10 0 0
tyr:1*yr
.EQN 0 10 0 0
rb:1*(ly)/(yr)
.TXT 4 -53 0 0
Cg a72.875000,73.000000,416
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {There are 11 variables of interest,
 at least three of which must be specified
 in order to get the other 8.  Since there
 are 10 different combinations of those 
three initial variables within each of the
 three kinematics, we provide an index j=0,2*9
 to be used later in summarizing results
 from any one of those 10 setup choices.
  We initialize the variables to arbitrary
 values in defining them at this point...}}
}
.EQN 9 1 0 0
j:0,1;2*9
.TXT 0 11 0 0
Cg a12.125000,51.000000,20
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {distance traveled}}
}
.EQN 0 17 0 0
{0:\Dx.j}NAME:0*m
.TXT 0 16 0 0
Cg a15.500000,28.000000,24
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {constant acceleration}}
}
.EQN 0 17 0 0
(ao)[(j):0*(m)/((sec)^(2))
.TXT 3 -62 0 0
Cg a36.875000,73.000000,52
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Newtonian (Low-Velocity Approximation)
 Variables:}}
}
.TXT 3 1 0 0
Cg a9.250000,72.000000,15
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {time elapsed}}
}
.EQN 0 10 0 0
({0:\Dt}NAME)[(j):0*sec
.TXT 0 12 0 0
Cg a9.625000,50.000000,19
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {initial velocity}}
}
.EQN 0 12 0 0
(vo)[(j):0*(m)/(sec)
.TXT 0 12 0 0
Cg a8.750000,26.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {final velocity}}
}
.EQN 0 12 0 0
(vf)[(j):0*(m)/(sec)
.TXT 3 -59 0 0
Cg a41.125000,73.000000,62
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Inertial Relativistic (Non-Accelerated
 Observer) Variables:}}
}
.TXT 3 1 0 0
Cg a9.250000,72.000000,15
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {time elapsed}}
}
.EQN 0 10 0 0
({0:\Db}NAME)[(j):0*iyr
.TXT 0 12 0 0
Cg a9.625000,50.000000,19
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {initial velocity}}
}
.EQN 0 12 0 0
(wo)[(j):0*c
.TXT 0 12 0 0
Cg a8.750000,26.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {final velocity}}
}
.EQN 0 12 0 0
(wf)[(j):0*c
.TXT 3 -59 0 0
Cg a49.125000,73.000000,71
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Traveler (Accelerated Observer 
or Proper-Time/4-Velocity) Variables:}}
}
.TXT 3 1 0 0
Cg a9.250000,72.000000,15
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {time elapsed}}
}
.EQN 0 10 0 0
({0:\D\t}NAME)[(j):0*tyr
.TXT 0 12 0 0
Cg a9.625000,50.000000,19
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {initial velocity}}
}
.EQN 0 12 0 0
(uo)[(j):0*rb
.TXT 0 12 0 0
Cg a8.750000,26.000000,17
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {final velocity}}
}
.EQN 0 12 0 0
(uf)[(j):0*rb
.TXT 4 -59 0 0
Cg a62.750000,72.000000,78
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs28 \ul Accelerated Frame,
 Traveler, or Proper-Time/4-Velocity Inputs}}
}
.TXT 4 0 0 0
Cg a73.000000,73.000000,395
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Initially, let's assume that the
 time-related variables (specifically time-elapsed
 and initial/final velocities) are specified
 in terms of the Proper Time kinematic. 
 This time-parameterization follows clocks
 of the accelerated observer, but disagrees
 with inertial observer clocks for velocities
 near the speed of light.  Some useful functions
 }{\i given accelerated frame Inputs}{ are:
  }}
}
.EQN 10 0 0 0
{0:\h}NAME(u):asinh((u)/(c))
.EQN 0 16 0 0
w(u):c*tanh({0:\h}NAME(u))
.EQN 0 18 0 0
{0:\g}NAME(u):cosh({0:\h}NAME(u))
.EQN 0 18 0 0
v(u):u*\((2)/({0:\g}NAME(u)+1))
.TXT 2 -17 0 0
Cg a17.750000,36.000000,35
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {^}{\i relativistic energy factor}}
}
.TXT 1 -34 0 0
Cg a18.250000,72.000000,34
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {^}{\i hyperbolic velocity angle}}
}
.TXT 3 -1 0 0
Cg a15.625000,33.000000,25
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Inertial Time Elapsed:}}
}
.EQN 0 19 0 0
Db(ao,uf,uo,{0:\Dx}NAME,{0:\D\t}NAME):if(ao{56}0*(m)/((sec)^(2)),(uf-uo)/(ao),{0:\D\t}NAME*{0:\g}NAME(uo))
.TXT 6 -19 0 0
Cg a18.250000,19.000000,18
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Newtonian Time:}}
}
.EQN 0 14 0 0
Dt(ao,uf,uo,{0:\Dx}NAME,{0:\D\t}NAME):if(ao{56}0*(m)/((sec)^(2)),(v(uf)-v(uo))/(ao),if(uo{56}0*(m)/(sec),({0:\Dx}NAME)/(v(uo)),{0:\D\t}NAME))
.TXT 5 -14 0 0
Cg a32.250000,38.625000,81
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 0:  I}{\f0 \fs24 
\b nputs are uo, uf, and ao}{\f0 \fs24 \b 
:}}
}
.TXT 0 33 0 0
Cg a38.125000,40.000000,51
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. traveler time for a 1g retrostop
 from rb 2?}}
}
.TXT 3 -32 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
(uo)[(0):4*rb
.EQN 0 22 0 0
(uf)[(0):0*rb
.EQN 0 23 0 0
(ao)[(0):-1*g
.TXT 4 -51 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 0 10 0 0
({0:\D\t}NAME)[(0):({0:\h}NAME((uf)[(0))-{0:\h}NAME((uo)[(0)))*(c)/((ao)[(0))
.EQN 0 25 0 0
({0:\Dx}NAME)[(0):({0:\g}NAME((uf)[(0))-{0:\g}NAME((uo)[(0)))*((c)^(2))/((ao)[(0))
.TXT 5 -36 0 0
Cg a33.250000,38.625000,111
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 1:  I}{\f0 \fs24 
\b nputs are }{\f1 \fs24 \b Dt}{\f0 \fs24 
\b , uo, and ao}{\f0 \fs24 \b :}}
}
.TXT 0 33 0 0
Cg a39.500000,42.625000,60
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. distance after 20 traveler-years
 of 1g acceleration?}}
}
.TXT 3 -32 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\D\t}NAME)[(1):20*yr
.EQN 0 22 0 0
(uo)[(1):0*rb
.EQN 0 24 0 0
(ao)[(1):1*g
.TXT 4 -52 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 1 10 0 0
(uf)[(1):c*sinh({0:\h}NAME((uo)[(1))+((ao)[(1)*({0:\D\t}NAME)[(1))/(c))
.EQN 0 26 0 0
({0:\Dx}NAME)[(1):({0:\g}NAME((uf)[(1))-{0:\g}NAME((uo)[(1)))*((c)^(2))/((ao)[(1))
.TXT 5 -37 0 0
Cg a33.875000,38.625000,111
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 2:  I}{\f0 \fs24 
\b nputs are }{\f1 \fs24 \b Dt}{\f0 \fs24 
\b , uf, and ao}{\f0 \fs24 \b :}}
}
.TXT 0 34 0 0
Cg a38.500000,39.000000,51
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. rb requiring 6 months of 1g
 retros to stop?}}
}
.TXT 3 -33 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\D\t}NAME)[(2):0.5*yr
.EQN 0 23 0 0
(uf)[(2):0*rb
.EQN 0 25 0 0
(ao)[(2):-1*g
.TXT 4 -54 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 1 9 0 0
(uo)[(2):c*sinh({0:\h}NAME((uf)[(2))-((ao)[(2)*({0:\D\t}NAME)[(2))/(c))
.EQN 0 27 0 0
({0:\Dx}NAME)[(2):({0:\g}NAME((uf)[(2))-{0:\g}NAME((uo)[(2)))*((c)^(2))/((ao)[(2))
.TXT 10 -37 0 0
C x1,1,0,0
.TXT 3 0 0 0
Cg a32.500000,38.625000,111
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 3:  I}{\f0 \fs24 
\b nputs are }{\f1 \fs24 \b Dt}{\f0 \fs24 
\b , uo, and uf}{\f0 \fs24 \b :}}
}
.TXT 0 33 0 0
Cg a38.250000,39.000000,46
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. how many gees for 0 to rb 
2 in 1 hour?}}
}
.TXT 3 -32 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\D\t}NAME)[(3):1*hr
.EQN 0 22 0 0
(uo)[(3):0*rb
.EQN 0 26 0 0
(uf)[(3):2*rb
.TXT 4 -54 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 0 10 0 0
(ao)[(3):({0:\h}NAME((uf)[(3))-{0:\h}NAME((uo)[(3)))*(c)/(({0:\D\t}NAME)[(3))
.EQN 0 25 0 0
({0:\Dx}NAME)[(3):({0:\g}NAME((uf)[(3))-{0:\g}NAME((uo)[(3)))*((c)^(2))/((ao)[(3))
.TXT 5 -35 0 0
Cg a33.000000,38.625000,111
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 4:  I}{\f0 \fs24 
\b nputs are }{\f1 \fs24 \b D}{\f0 \fs24 
\b x, uo, and ao}{\f0 \fs24 \b :}}
}
.TXT 0 34 0 0
Cg a35.625000,38.000000,54
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. times for a 1-g space dragster
 in a 4-ly race?}}
}
.TXT 3 -33 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dx}NAME)[(4):4*ly
.EQN 0 22 0 0
(uo)[(4):0*rb
.EQN 0 25 0 0
(ao)[(4):1*g
.TXT 2 -51 0 0
Cg a5.000000,69.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 4 -4 0 0
{0:\gf}NAME:{0:\g}NAME((uo)[(4))+({0:\Dx}NAME)[(4)*((ao)[(4))/((c)^(2))
.TXT 0 19 0 0
Cg a7.125000,54.000000,14
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {& either...}}
}
.EQN 0 10 0 0
(uf)[(4):c*\(({0:\gf}NAME)^(2)-1)
.EQN 0 17 0 0
({0:\D\t}NAME)[(4):({0:\h}NAME((uf)[(4))-{0:\h}NAME((uo)[(4)))*(c)/((ao)[(4))
.TXT 5 -27 0 0
Cg a2.875000,54.000000,8
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {or...}}
}
.EQN 0 10 0 0
(uf)[(14):-c*\(({0:\gf}NAME)^(2)-1)
.EQN 0 17 0 0
({0:\D\t}NAME)[(14):({0:\h}NAME((uf)[(14))-{0:\h}NAME((uo)[(4)))*(c)/((ao)[(4))
.TXT 5 -45 0 0
Cg a32.750000,38.625000,111
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 5:  I}{\f0 \fs24 
\b nputs are }{\f1 \fs24 \b D}{\f0 \fs24 
\b x, uf, and ao}{\f0 \fs24 \b :}}
}
.TXT 0 34 0 0
Cg a37.625000,38.000000,69
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Traveler time for 1g retrostop 
over the 4-ly to }{\f1 \fs20 a}{-C?}}
}
.TXT 3 -33 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dx}NAME)[(5):4*ly
.EQN 0 22 0 0
(uf)[(5):0*rb
.EQN 0 24 0 0
(ao)[(5):-1*g
.TXT 3 -50 0 0
Cg a5.000000,69.000000,7
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then}}
}
.EQN 4 -4 0 0
{0:\go}NAME:{0:\g}NAME((uf)[(5))-({0:\Dx}NAME)[(5)*((ao)[(5))/((c)^(2))
.TXT 0 18 0 0
Cg a7.125000,55.000000,14
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {& either...}}
}
.EQN 0 10 0 0
(uo)[(5):c*\(({0:\go}NAME)^(2)-1)
.EQN 0 19 0 0
({0:\D\t}NAME)[(5):({0:\h}NAME((uf)[(5))-{0:\h}NAME((uo)[(5)))*(c)/((ao)[(5))
.TXT 6 -29 0 0
Cg a2.875000,55.000000,8
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {or...}}
}
.EQN 0 10 0 0
(uo)[(15):c*\(({0:\go}NAME)^(2)-1)
.EQN 0 19 0 0
({0:\D\t}NAME)[(15):({0:\h}NAME((uf)[(5))-{0:\h}NAME((uo)[(15)))*(c)/((ao)[(5))
.TXT 5 -47 0 0
Cg a32.625000,38.625000,111
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 6:  I}{\f0 \fs24 
\b nputs are }{\f1 \fs24 \b D}{\f0 \fs24 
\b x, uo, and uf}{\f0 \fs24 \b :}}
}
.TXT 0 34 0 0
Cg a30.500000,39.000000,45
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. retrodecel for a 1-ly stop
 from rb 2?}}
}
.TXT 3 -33 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\Dx}NAME)[(6):1*ly
.EQN 0 24 0 0
(uo)[(6):2*rb
.EQN 0 23 0 0
(uf)[(6):0*rb
.TXT 4 -53 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 1 10 0 0
(ao)[(6):(({0:\g}NAME((uf)[(6)))^(2)-({0:\g}NAME((uo)[(6)))^(2))*((c)^(2))/(({0:\Dx}NAME)[(6))
.EQN 0 29 0 0
({0:\D\t}NAME)[(6):({0:\h}NAME((uf)[(6))-{0:\h}NAME((uo)[(6)))*(c)/((ao)[(6))
.TXT 5 -40 0 0
Cg a33.250000,38.625000,154
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 7:  I}{\f0 \fs24 
\b nputs are }{\f1 \fs24 \b Dt}{\f0 \fs24 
\b , }{\f0 \fs24 \b \f1 \fs24 \b D}{\f0 
\fs24 \b x, and ao}{\f0 \fs24 \b :}}
}
.TXT 0 34 0 0
Cg a38.375000,39.000000,56
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. start speed needed for 1g 
burn over 1 ly in 1yr?}}
}
.TXT 3 -34 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 6 0 0
({0:\D\t}NAME)[(7):1*tyr
.EQN 0 28 0 0
({0:\Dx}NAME)[(7):1*ly
.EQN 0 22 0 0
(ao)[(7):1*g
.TXT 3 -56 0 0
Cg a5.000000,72.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 2 6 0 0
{0:\hav}NAME:asinh(((ao)[(7)*({0:\Dx}NAME)[(7))/(2*(c)^(2)*sinh(((ao)[(7)*({0:\D\t}NAME)[(7))/(2*c))))
.EQN 0 25 0 0
(uo)[(7):c*sinh({0:\hav}NAME-((ao)[(7)*({0:\D\t}NAME)[(7))/(2*c))
.EQN 0 22 0 0
(uf)[(7):c*sinh({0:\hav}NAME+((ao)[(7)*({0:\D\t}NAME)[(7))/(2*c))
.TXT 8 -53 0 0
Cg a35.125000,38.625000,141
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 8:  I}{\f0 \fs24 
\b nputs are }{\f1 \fs24 \b Dt}{\f0 \fs24 
\b , }{\f1 \fs24 \b D}{\f0 \fs24 \b x, and
 uo}{\f0 \fs24 \b :}}
}
.TXT 0 34 0 0
Cg a37.500000,38.000000,67
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. rb speed after a 5-tyear burn
 to }{\f1 \fs20 a}{-Centauri? }}
}
.TXT 3 -34 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 7 0 0
({0:\D\t}NAME)[(8):5*tyr
.EQN 0 22 0 0
({0:\Dx}NAME)[(8):4*ly
.EQN 0 21 0 0
(uo)[(8):0*rb
.TXT 4 -50 0 0
Cg a4.625000,64.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Define}}
}
.EQN 0 5 0 0
f({0:\h}NAME):cosh({0:\h}NAME)-({0:\h}NAME*({0:\Dx}NAME)[(8))/(c*({0:\D\t}NAME)[(8))
.EQN 0 18 0 0
{0:\ho}NAME:{0:\h}NAME((uo)[(8))
.TXT 0 10 0 0
Cg a6.250000,38.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Guess:}}
}
.EQN 0 5 0 0
x:(2*({0:\Dx}NAME)[(8))/(c*({0:\D\t}NAME)[(8))-{0:\ho}NAME
.TXT 0 12 0 0
Cg a5.500000,5.500000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Solve:}}
}
.EQN 0 5 0 0
{0:\hf}NAME:root(f(x)-f({0:\ho}NAME),x)
.TXT 5 -54 0 0
Cg a5.000000,73.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 0 23 0 0
(uf)[(8):c*sinh({0:\hf}NAME)
.EQN 0 24 0 0
(ao)[(8):({0:\hf}NAME-{0:\ho}NAME)*(c)/(({0:\D\t}NAME)[(8))
.TXT 5 -48 0 0
Cg a35.125000,38.625000,141
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs24 \b Case 9:  I}{\f0 \fs24 
\b nputs are }{\f1 \fs24 \b Dt}{\f0 \fs24 
\b , }{\f1 \fs24 \b D}{\f0 \fs24 \b x, and
 uf}{\f0 \fs24 \b :}}
}
.TXT 0 35 0 0
Cg a37.500000,38.000000,69
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {e.g. decel for a 5-tyear retrostop
 from }{\f1 \fs20 a}{-Centauri? }}
}
.TXT 3 -35 0 0
Cg a4.500000,73.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Given:}}
}
.EQN 0 7 0 0
({0:\D\t}NAME)[(9):5*tyr
.EQN 0 22 0 0
({0:\Dx}NAME)[(9):4*ly
.EQN 0 21 0 0
(uf)[(9):0*rb
.TXT 4 -50 0 0
Cg a4.625000,64.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Define}}
}
.EQN 0 5 0 0
f({0:\h}NAME):cosh({0:\h}NAME)-({0:\h}NAME*({0:\Dx}NAME)[(9))/(c*({0:\D\t}NAME)[(9))
.EQN 0 18 0 0
{0:\hf}NAME:{0:\h}NAME((uf)[(9))
.TXT 0 10 0 0
Cg a6.250000,38.000000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Guess:}}
}
.EQN 0 5 0 0
x:(2*({0:\Dx}NAME)[(9))/(c*({0:\D\t}NAME)[(9))-{0:\hf}NAME
.TXT 0 11 0 0
Cg a5.500000,5.500000,9
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Solve:}}
}
.EQN 0 6 0 0
{0:\ho}NAME:root(f(x)-f({0:\hf}NAME),x)
.TXT 5 -54 0 0
Cg a5.000000,73.000000,10
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Then...}}
}
.EQN 0 23 0 0
(uo)[(9):c*sinh({0:\ho}NAME)
.EQN 0 25 0 0
(ao)[(9):({0:\hf}NAME-{0:\ho}NAME)*(c)/(({0:\D\t}NAME)[(9))
.TXT 10 -49 0 0
C x1,1,0,0
.TXT 8 0 0 0
Cg a47.750000,73.000000,77
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\ul \f0 \fs28 \b Results Report
 - Accelerated Frame Inputs}{\f0 \fs28 \b 
:}}
}
.TXT 0 48 0 0
Cg a14.500000,71.000000,22
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\i For Case Number:}}
}
.EQN 0 16 0 0
i:4
.TXT 4 -63 0 0
Cg a66.750000,72.000000,77
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Variables which are Independent
 of Kinematic or Time-Parameterization are:}}
}
.TXT 3 2 0 0
Cg a6.875000,68.000000,12
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Distance:}}
}
.EQN 0 8 0 0
({0:\Dx}NAME)[(i)=?ly
.TXT 0 24 0 0
Cg a16.500000,47.000000,25
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Constant Acceleration:}}
}
.EQN 0 17 0 0
(ao)[(i)=?g
.TXT 4 -51 0 0
Cg a71.750000,72.000000,79
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Traveler (Accelerated Observer)
 Vector 4-Velocities and Elapsed Proper-Time:}}
}
.EQN 4 0 0 0
(uo)[(i)=?rb
.EQN 0 22 0 0
(uf)[(i)=?rb
.EQN 0 22 0 0
({0:\D\t}NAME)[(i)=?tyr
.TXT 4 -44 0 0
Cg a51.875000,72.000000,76
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Inertial Relativistic (Non-Accelerated
 Observer) Velocities/Elapsed-Time:}}
}
.EQN 3 0 0 0
(wo)[(i):w((uo)[(i))
.EQN 0 22 0 0
(wf)[(i):w((uf)[(i))
.EQN 0 22 0 0
({0:\Db}NAME)[(i):Db((ao)[(i),(uf)[(i),(uo)[(i),({0:\Dx}NAME)[(i),({0:\D\t}NAME)[(i))
.EQN 3 -44 0 0
(wo)[(i)=?c
.EQN 0 22 0 0
(wf)[(i)=?c
.EQN 0 22 0 0
({0:\Db}NAME)[(i)=?iyr
.TXT 3 -44 0 0
Cg a47.625000,72.000000,66
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Newtonian (Low-Velocity Approximation)
 Velocities/Elapsed-Time:}}
}
.EQN 3 0 0 0
(vo)[(i):v((uo)[(i))
.EQN 0 22 0 0
(vf)[(i):v((uf)[(i))
.EQN 0 22 0 0
({0:\Dt}NAME)[(i):Dt((ao)[(i),(uf)[(i),(uo)[(i),({0:\Dx}NAME)[(i),({0:\D\t}NAME)[(i))
.EQN 3 -44 0 0
(vo)[(i)=?(m)/(sec)
.EQN 1 22 0 0
(vf)[(i)=?(m)/(sec)
.EQN 0 22 0 0
({0:\Dt}NAME)[(i)=?sec
.TXT 6 -45 0 0
Cg a27.875000,73.000000,39
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs28 Some Graphs of the Result:}}
}
.EQN 4 12 0 0
uT({0:\t}NAME):c*sinh({0:\h}NAME((uo)[(i))+((ao)[(i)*{0:\t}NAME)/(c))
.EQN 0 25 0 0
x({0:\t}NAME):({0:\g}NAME(uT({0:\t}NAME))-{0:\g}NAME((uo)[(i)))*((c)^(2))/((ao)[(i))
.EQN 5 -17 0 0
wT({0:\t}NAME):w(uT({0:\t}NAME))
.EQN 0 17 0 0
b({0:\t}NAME):Db((ao)[(i),uT({0:\t}NAME),(uo)[(i),x({0:\t}NAME),{0:\t}NAME)
.EQN 5 -17 0 0
vT({0:\t}NAME):v(uT({0:\t}NAME))
.EQN 0 17 0 0
t({0:\t}NAME):Dt((ao)[(i),uT({0:\t}NAME),(uo)[(i),x({0:\t}NAME),{0:\t}NAME)
.EQN 5 -12 0 0
{0:\tInc}NAME:(({0:\D\t}NAME)[(i))/(100)
.EQN 0 12 0 0
{0:\t}NAME:0*sec,{0:\tInc}NAME;({0:\D\t}NAME)[(i)
.EQN 3 -37 0 0
&&b({0:\t}NAME),t({0:\t}NAME),{0:\t}NAME@&&x({0:\t}NAME)
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 24 18
.EQN 0 39 0 0
&&wT({0:\t}NAME),vT({0:\t}NAME),uT({0:\t}NAME)@&&x({0:\t}NAME)
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 18
.EQN 26 -37 0 0
&&b({0:\t}NAME),t({0:\t}NAME),{0:\t}NAME@&&{0:\t}NAME
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 17
.EQN 0 37 0 0
&&wT({0:\t}NAME),vT({0:\t}NAME),uT({0:\t}NAME)@&&{0:\t}NAME
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 20 17
.TXT 25 -39 0 0
C x1,1,0,0
.TXT 5 0 0 0
Cg a71.500000,72.000000,95
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {For Cases with i=4,5, a Set of 
Different Kinematic-Dependent Values may
 also Fit the Inputs:}}
}
.TXT 5 3 0 0
Cg a31.750000,69.000000,48
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {We first set up the Alternative
 Value Arrays:}}
}
.EQN 0 39 0 0
k:0,1;9
.EQN 3 -43 0 0
(vo)[(k+10):if(k÷5,(vo)[(k+10),(vo)[(k))
.EQN 0 22 0 0
(vf)[(k+10):if(k÷4,(vf)[(k+10),(vf)[(k))
.EQN 0 21 0 0
({0:\Dt}NAME)[(k+10):if(k<4,({0:\Dt}NAME)[(k),if(k>6,({0:\Dt}NAME)[(k),({0:\Dt}NAME)[(k+10)))
.TXT 5 -39 0 0
Cg a31.500000,71.000000,48
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {The Alternative Value Index for
 this Case is:}}
}
.EQN 0 33 0 0
k:i+10
.TXT 0 10 0 0
Cg a17.375000,26.000000,26
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {which has Values for...}}
}
.TXT 3 -46 0 0
Cg a71.750000,72.000000,79
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Traveler (Accelerated Observer)
 Vector 4-Velocities and Elapsed Proper-Time:}}
}
.EQN 4 0 0 0
(uo)[(k)=?rb
.EQN 0 22 0 0
(uf)[(k)=?rb
.EQN 0 22 0 0
({0:\D\t}NAME)[(k)=?tyr
.TXT 4 -44 0 0
Cg a51.875000,72.000000,76
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Inertial Relativistic (Non-Accelerated
 Observer) Velocities/Elapsed-Time:}}
}
.EQN 3 0 0 0
(wo)[(k):w((uo)[(k))
.EQN 0 22 0 0
(wf)[(k):w((uf)[(k))
.EQN 0 22 0 0
({0:\Db}NAME)[(k):Db((ao)[(i),(uf)[(k),(uo)[(k),({0:\Dx}NAME)[(i),({0:\D\t}NAME)[(k))
.EQN 3 -44 0 0
(wo)[(k)=?c
.EQN 0 22 0 0
(wf)[(k)=?c
.EQN 0 22 0 0
({0:\Db}NAME)[(k)=?iyr
.TXT 3 -44 0 0
Cg a47.625000,72.000000,66
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {Newtonian (Low-Velocity Approximation)
 Velocities/Elapsed-Time:}}
}
.EQN 3 0 0 0
(vo)[(k):v((uo)[(k))
.EQN 0 22 0 0
(vf)[(k):v((uf)[(k))
.EQN 0 22 0 0
({0:\Dt}NAME)[(k):Dt((ao)[(i),(uf)[(k),(uo)[(k),({0:\Dx}NAME)[(i),({0:\D\t}NAME)[(k))
.EQN 3 -44 0 0
(vo)[(k)=?(m)/(sec)
.EQN 1 22 0 0
(vf)[(k)=?(m)/(sec)
.EQN 0 22 0 0
({0:\Dt}NAME)[(k)=?sec
.TXT 6 -45 0 0
Cg a27.875000,73.000000,39
{\rtf1\ansi \deff0
{\fonttbl
{\f0\fnil Arial;}
{\f1\fnil Symbol;}
}
{\plain {\f0 \fs28 Some Graphs of the Result:}}
}
.EQN 4 12 0 0
uT({0:\t}NAME):c*sinh({0:\h}NAME((uo)[(k))+((ao)[(i)*{0:\t}NAME)/(c))
.EQN 0 25 0 0
x({0:\t}NAME):({0:\g}NAME(uT({0:\t}NAME))-{0:\g}NAME((uo)[(k)))*((c)^(2))/((ao)[(i))
.EQN 5 -17 0 0
wT({0:\t}NAME):w(uT({0:\t}NAME))
.EQN 0 17 0 0
b({0:\t}NAME):Db((ao)[(i),uT({0:\t}NAME),(uo)[(k),x({0:\t}NAME),{0:\t}NAME)
.EQN 5 -17 0 0
vT({0:\t}NAME):v(uT({0:\t}NAME))
.EQN 0 17 0 0
t({0:\t}NAME):Dt((ao)[(i),uT({0:\t}NAME),(uo)[(k),x({0:\t}NAME),{0:\t}NAME)
.EQN 5 -12 0 0
{0:\tInc}NAME:(({0:\D\t}NAME)[(k))/(100)
.EQN 0 12 0 0
{0:\t}NAME:0*sec,{0:\tInc}NAME;({0:\D\t}NAME)[(k)
.EQN 3 -37 0 0
_n_u_l_l_&_n_u_l_l_&b({0:\t}NAME),t({0:\t}NAME),{0:\t}NAME@_n_u_l_l_&_n_u_l_l_&x({0:\t}NAME)
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 24 18
.EQN 0 39 0 0
_n_u_l_l_&_n_u_l_l_&wT({0:\t}NAME),vT({0:\t}NAME),uT({0:\t}NAME)@_n_u_l_l_&_n_u_l_l_&x({0:\t}NAME)
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 18
.EQN 26 -37 0 0
_n_u_l_l_&_n_u_l_l_&b({0:\t}NAME),t({0:\t}NAME),{0:\t}NAME@_n_u_l_l_&_n_u_l_l_&{0:\t}NAME
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 21 17
.EQN 0 37 0 0
_n_u_l_l_&_n_u_l_l_&wT({0:\t}NAME),vT({0:\t}NAME),uT({0:\t}NAME)@_n_u_l_l_&_n_u_l_l_&{0:\t}NAME
0 0 1 1 0
0 0 1 1 0
0 1 0 0 NO-TRACE-STRING
0 2 1 0 NO-TRACE-STRING
0 3 2 0 NO-TRACE-STRING
0 4 3 0 NO-TRACE-STRING
0 1 4 0 NO-TRACE-STRING
0 2 5 0 NO-TRACE-STRING
0 3 6 0 NO-TRACE-STRING
0 4 0 0 NO-TRACE-STRING
0 1 1 0 NO-TRACE-STRING
0 2 2 0 NO-TRACE-STRING
0 3 3 0 NO-TRACE-STRING
0 4 4 0 NO-TRACE-STRING
0 1 5 0 NO-TRACE-STRING
0 2 6 0 NO-TRACE-STRING
0 3 0 0 NO-TRACE-STRING
0 4 1 0 NO-TRACE-STRING
0 1 20 17