.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: 12 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 a73.000000,73.000000,417 {\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 the input kinematic used here, 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 a54.750000,72.000000,73 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\f0 \fs28 \ul Inertial Relativistic (or UnAccelerated Observer) Inputs}} } .TXT 3 0 0 0 Cg a73.000000,73.000000,407 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {A}{ssume here that the time-related variables (specifically time-elapsed and initial/final velocities) are specified in terms of the inertial relativistic kinematic. This time-parameterization follows the clocks of an inertial observer, but disagrees with accelerated observer clocks for velocities near the speed of light. Some useful functions }{\i given }{\i inertial relativistic inputs}{ are: }} } .EQN 10 0 0 0 {0:\g}NAME(w):\((1)/(1-(((w)/(c)))^(2))) .EQN 0 18 0 0 u(w):w*{0:\g}NAME(w) .EQN 0 16 0 0 v(w):u(w)*\((2)/({0:\g}NAME(w)+1)) .EQN 0 21 0 0 {0:\h}NAME(w):atanh((w)/(c)) .TXT 3 -40 0 0 Cg a19.625000,58.000000,37 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {<= }{\i relativistic energy factor}} } .TXT 1 23 0 0 Cg a18.250000,20.500000,34 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\i hyperbolic velocity angle}{^}} } .TXT 4 -38 0 0 Cg a12.000000,72.000000,18 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Newtonian Time:}} } .EQN 0 13 0 0 Dt(ao,wf,wo,{0:\Dx}NAME,{0:\Db}NAME):if(ao{56}0*(m)/((sec)^(2)),(v(wf)-v(wo))/(ao),if(u(wo){56}0*(m)/(sec),({0:\Dx}NAME)/(v(wo)),{0:\Db}NAME)) .TXT 6 -13 0 0 Cg a9.250000,73.000000,15 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Proper Time:}} } .EQN 0 10 0 0 {0:D\t}NAME(ao,wf,wo,{0:\Dx}NAME,{0:\Db}NAME):if(ao{56}0*(m)/((sec)^(2)),({0:\h}NAME(wf)-{0:\h}NAME(wo))/(ao)*c,if(u(wo){56}0*(m)/(sec),({0:\Dx}NAME)/(u(wo)),{0:\Db}NAME)) .TXT 5 -10 0 0 Cg a32.750000,38.625000,81 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\f0 \fs24 \b Case 0: I}{\f0 \fs24 \b nputs are wo, wf, and ao}{\f0 \fs24 \b :}} } .TXT 0 33 0 0 Cg a37.375000,40.000000,57 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {e.g. inertial time needed for 1g startup-burn to 0.9c?}} } .TXT 2 -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 (wo)[(0):0*c .EQN 0 24 0 0 (wf)[(0):.9*c .EQN 0 24 0 0 (ao)[(0):1*g .EQN 4 -41 0 0 ({0:\Db}NAME)[(0):(u((wf)[(0))-u((wo)[(0)))/((ao)[(0)) .EQN 0 24 0 0 ({0:\Dx}NAME)[(0):({0:\g}NAME((wf)[(0))-{0:\g}NAME((wo)[(0)))/((ao)[(0))*(c)^(2) .TXT 1 -37 0 0 Cg a5.000000,72.000000,10 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Then...}} } .TXT 4 -1 0 0 Cg a33.375000,38.625000,111 {\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 D}{\f0 \fs24 \b b, wo, and ao}{\f0 \fs24 \b :}} } .TXT 0 34 0 0 Cg a38.500000,39.000000,58 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {e.g. expedition distance after 20 earth yrs of 1g-burn?}} } .TXT 2 -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:\Db}NAME)[(1):20*iyr .EQN 0 24 0 0 (wo)[(1):0*c .EQN 0 23 0 0 (ao)[(1):1*g .TXT 4 -53 0 0 Cg a5.000000,72.000000,10 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Then...}} } .EQN 0 11 0 0 (wf)[(1):(u((wo)[(1))+(ao)[(1)*({0:\Db}NAME)[(1))/(\(1+(((u((wo)[(1))+(ao)[(1)*({0:\Db}NAME)[(1))/(c)))^(2))) .EQN 0 26 0 0 ({0:\Dx}NAME)[(1):({0:\g}NAME((wf)[(1))-{0:\g}NAME((wo)[(1)))/((ao)[(1))*(c)^(2) .TXT 9 -38 0 0 Cg a32.875000,38.625000,111 {\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 D}{\f0 \fs24 \b b, wf, and ao}{\f0 \fs24 \b :}} } .TXT 0 33 0 0 Cg a39.625000,40.000000,55 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {e.g. speed requiring an iyr of 1g-retroburn to stop?}} } .TXT 2 -33 0 0 Cg a4.500000,73.000000,9 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Given:}} } .EQN 0 8 0 0 ({0:\Db}NAME)[(2):1*iyr .EQN 0 24 0 0 (wf)[(2):0*c .EQN 0 23 0 0 (ao)[(2):-1*g .TXT 3 -55 0 0 Cg a5.000000,72.000000,10 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Then...}} } .EQN 1 12 0 0 (wo)[(2):(u((wf)[(2))-(ao)[(2)*({0:\Db}NAME)[(2))/(\(1+(((u((wf)[(2))-(ao)[(2)*({0:\Db}NAME)[(2))/(c)))^(2))) .EQN 0 26 0 0 ({0:\Dx}NAME)[(2):({0:\g}NAME((wf)[(2))-{0:\g}NAME((wo)[(2)))/((ao)[(2))*(c)^(2) .TXT 10 -38 0 0 C x1,1,0,0 .TXT 3 0 0 0 Cg a34.250000,38.625000,124 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\f0 \fs24 \b Case 3: I}{\f0 \fs24 \b nputs are }{\f0 \fs24 \b \f1 \fs24 \b D}{\f0 \fs24 \b b, wo, and wf}{\f0 \fs24 \b :}} } .TXT 0 35 0 0 Cg a26.500000,38.000000,41 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {e.g. 'gees' to do 0 to 0.9c in 1 week?}} } .TXT 2 -35 0 0 Cg a4.500000,73.000000,9 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Given:}} } .EQN 0 8 0 0 ({0:\Db}NAME)[(3):7*day .EQN 0 24 0 0 (wo)[(3):0*c .EQN 0 24 0 0 (wf)[(3):0.9*c .TXT 4 -55 0 0 Cg a5.000000,72.000000,10 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Then...}} } .EQN 0 14 0 0 (ao)[(3):(u((wf)[(3))-u((wo)[(3)))/(({0:\Db}NAME)[(3)) .EQN 0 23 0 0 ({0:\Dx}NAME)[(3):({0:\g}NAME((wf)[(3))-{0:\g}NAME((wo)[(3)))/((ao)[(3))*(c)^(2) .TXT 5 -38 0 0 Cg a33.250000,38.625000,124 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\f0 \fs24 \b Case 4: I}{\f0 \fs24 \b nputs are }{\f0 \fs24 \b \f1 \fs24 \b D}{\f0 \fs24 \b x, wo, and ao}{\f0 \fs24 \b :}} } .TXT 0 34 0 0 Cg a38.375000,39.000000,60 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {e.g. earthtime for a 1-g space dragster in a 4-ly race}{?}} } .TXT 2 -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 26 0 0 (wo)[(4):0*c .EQN 0 24 0 0 (ao)[(4):1*g .TXT 2 -55 0 0 Cg a5.000000,71.000000,10 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Then...}} } .EQN 4 -2 0 0 {0:\gf}NAME:{0:\g}NAME((wo)[(4))+({0:\Dx}NAME)[(4)*((ao)[(4))/((c)^(2)) .TXT 0 17 0 0 Cg a11.250000,72.000000,13 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {& }{either}} } .EQN 0 8 0 0 (wf)[(4):(\(({0:\gf}NAME)^(2)-1))/({0:\gf}NAME)*c .EQN 0 16 0 0 ({0:\Db}NAME)[(4):(u((wf)[(4))-u((wo)[(4)))/((ao)[(4)) .TXT 7 -24 0 0 Cg a3.875000,70.000000,10 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {or}{...}} } .EQN 0 7 0 0 (wf)[(14):-((\(({0:\gf}NAME)^(2)-1))/({0:\gf}NAME))*c .EQN 0 17 0 0 ({0:\Db}NAME)[(14):(u((wf)[(14))-u((wo)[(4)))/((ao)[(4)) .TXT 5 -41 0 0 Cg a33.125000,38.625000,124 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\f0 \fs24 \b Case 5: I}{\f0 \fs24 \b nputs are }{\f0 \fs24 \b \f1 \fs24 \b D}{\f0 \fs24 \b x, wf, and ao}{\f0 \fs24 \b :}} } .TXT 0 33 0 0 Cg a37.875000,40.000000,69 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {e.g. earth time for a 1g retrostop to }{\f1 \fs20 a}{-C over 1-ly?}} } .TXT 2 -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:\Dx}NAME)[(5):2*ly .EQN 0 27 0 0 (wf)[(5):0*c .EQN 0 24 0 0 (ao)[(5):-1*g .TXT 2 -56 0 0 Cg a5.000000,71.000000,10 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Then...}} } .EQN 4 -2 0 0 {0:\go}NAME:{0:\g}NAME((wf)[(5))-({0:\Dx}NAME)[(5)*((ao)[(5))/((c)^(2)) .TXT 0 17 0 0 Cg a5.875000,56.000000,11 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {& either}} } .EQN 0 7 0 0 (wo)[(5):(\(({0:\go}NAME)^(2)-1))/({0:\go}NAME)*c .EQN 0 17 0 0 ({0:\Db}NAME)[(5):(u((wf)[(5))-u((wo)[(5)))/((ao)[(5)) .TXT 7 -24 0 0 Cg a2.875000,64.000000,8 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {or...}} } .EQN 0 7 0 0 (wo)[(15):-((\(({0:\go}NAME)^(2)-1))/({0:\go}NAME))*c .EQN 0 17 0 0 ({0:\Db}NAME)[(15):(u((wf)[(5))-u((wo)[(15)))/((ao)[(5)) .TXT 5 -41 0 0 Cg a33.250000,38.625000,111 {\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, wo, and wf}{\f0 \fs24 \b :}} } .TXT 0 33 0 0 Cg a33.750000,40.000000,52 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {e.g. retrodeceleration for a 1-ly stop from 0.9c?}} } .TXT 2 -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:\Dx}NAME)[(6):1*ly .EQN 0 27 0 0 (wo)[(6):0*c .EQN 0 24 0 0 (wf)[(6):.9*c .TXT 4 -57 0 0 Cg a5.000000,72.000000,10 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Then...}} } .EQN 0 13 0 0 (ao)[(6):({0:\g}NAME((wf)[(6))-{0:\g}NAME((wo)[(6)))*((c)^(2))/(({0:\Dx}NAME)[(6)) .EQN 0 27 0 0 ({0:\Db}NAME)[(6):(u((wf)[(6))-u((wo)[(6)))/((ao)[(6)) .TXT 5 -41 0 0 Cg a35.875000,38.625000,225 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\f0 \fs24 \b Case 7: I}{\f0 \fs24 \b nputs are }{\f0 \fs24 \b \f0 \fs24 \b }{\f0 \fs24 \b \f1 \fs24 \b D}{\f0 \fs24 \b b, }{\f0 \fs24 \b \f0 \fs24 \b }{\f0 \fs24 \b \f1 \fs24 \b D}{\f0 \fs24 \b x, and ao}{\f0 \fs24 \b :}} } .TXT 0 35 0 0 Cg a36.750000,38.000000,57 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {e.g. start speed for a 1g, 1-ly burn in 1.5 earth yrs?}} } .TXT 2 -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:\Db}NAME)[(7):1.5*iyr .EQN 0 28 0 0 ({0:\Dx}NAME)[(7):1*ly .EQN 0 24 0 0 (ao)[(7):1*g .EQN 3 -40 0 0 Y:1-(((({0:\Dx}NAME)[(7))/(c*({0:\Db}NAME)[(7))))^(2) .EQN 0 25 0 0 Z:((((ao)[(7)*({0:\Db}NAME)[(7)*Y)/(2*c)))^(2) .TXT 2 -43 0 0 Cg a5.000000,72.000000,10 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Then...}} } .TXT 5 0 0 0 Cg a4.125000,72.000000,9 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {and...}} } .EQN 0 8 0 0 (wo)[(7):(({0:\Dx}NAME)[(7)-0.5*(ao)[(7)*((({0:\Db}NAME)[(7)))^(2)*Y*\(Y+Z))/(({0:\Db}NAME)[(7)*(1+Z)) .EQN 0 30 0 0 (wf)[(7):(({0:\Dx}NAME)[(7)+0.5*(ao)[(7)*((({0:\Db}NAME)[(7)))^(2)*Y*\(Y+Z))/(({0:\Db}NAME)[(7)*(1+Z)) .TXT 6 -39 0 0 Cg a34.250000,38.625000,193 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\f0 \fs24 \b Case 8: I}{\f0 \fs24 \b nputs are }{\f0 \fs24 \b \f0 \fs24 \b \f1 \fs24 \b D}{\f0 \fs24 \b b, }{\f0 \fs24 \b \f0 \fs24 \b \f1 \fs24 \b D}{\f0 \fs24 \b x, and wo}{\f0 \fs24 \b :}} } .TXT 0 34 0 0 Cg a38.750000,39.000000,68 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {e.g. accel during a 5 earth-yr startup burn 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:\Db}NAME)[(8):5*iyr .EQN 0 26 0 0 ({0:\Dx}NAME)[(8):4*ly .EQN 0 24 0 0 (wo)[(8):0*c .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 10 0 0 (ao)[(8):2*{0:\g}NAME((wo)[(8))*(({0:\Dx}NAME)[(8)-(wo)[(8)*({0:\Db}NAME)[(8))/(((({0:\Db}NAME)[(8)))^(2)-(((({0:\Dx}NAME)[(8))/(c)))^(2)) .EQN 0 28 0 0 (wf)[(8):(u((wo)[(8))+(ao)[(8)*({0:\Db}NAME)[(8))/(\(1+(((u((wo)[(8))+(ao)[(8)*({0:\Db}NAME)[(8))/(c)))^(2))) .TXT 10 -39 0 0 Cg a34.750000,38.625000,193 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\f0 \fs24 \b Case 9: I}{\f0 \fs24 \b nputs are }{\f0 \fs24 \b \f0 \fs24 \b \f1 \fs24 \b D}{\f0 \fs24 \b b, }{\f0 \fs24 \b \f0 \fs24 \b \f1 \fs24 \b D}{\f0 \fs24 \b x, and wf}{\f0 \fs24 \b :}} } .TXT 0 35 0 0 Cg a37.500000,39.000000,71 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {e.g. decel for a 5 earth-yr retrostop from }{\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 6 0 0 ({0:\Db}NAME)[(9):5*iyr .EQN 0 26 0 0 ({0:\Dx}NAME)[(9):4*ly .EQN 0 25 0 0 (wf)[(9):0*c .TXT 4 -57 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)[(9):-2*{0:\g}NAME((wf)[(9))*(({0:\Dx}NAME)[(9)-(wf)[(9)*({0:\Db}NAME)[(9))/(((({0:\Db}NAME)[(9)))^(2)-(((({0:\Dx}NAME)[(9))/(c)))^(2)) .EQN 0 27 0 0 (wo)[(9):(u((wf)[(9))-(ao)[(9)*({0:\Db}NAME)[(9))/(\(1+(((u((wf)[(9))-(ao)[(9)*({0:\Db}NAME)[(9))/(c)))^(2))) .TXT 14 -38 0 0 C x1,1,0,0 .TXT 8 0 0 0 Cg a51.750000,73.000000,81 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\ul \f0 \fs28 \b Results Report - Relativistic Inertial 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 17 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 -44 0 0 Cg a52.375000,72.000000,78 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Inertial Relativistic (Non-Accelerated Observer)}{ Velocities/Elapsed-Time:}} } .EQN 4 0 0 0 (wo)[(i)=?c .EQN 0 22 0 0 (wf)[(i)=?c .EQN 0 22 0 0 ({0:\Db}NAME)[(i)=?iyr .TXT 4 -44 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 3 0 0 0 (uo)[(i):u((wo)[(i)) .EQN 0 22 0 0 (uf)[(i):u((wf)[(i)) .EQN 0 22 0 0 ({0:\D\t}NAME)[(i):{0:D\t}NAME((ao)[(i),(wf)[(i),(wo)[(i),({0:\Dx}NAME)[(i),({0:\Db}NAME)[(i)) .EQN 3 -44 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 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((wo)[(i)) .EQN 0 22 0 0 (vf)[(i):v((wf)[(i)) .EQN 0 22 0 0 ({0:\Dt}NAME)[(i):Dt((ao)[(i),(wf)[(i),(wo)[(i),({0:\Dx}NAME)[(i),({0:\Db}NAME)[(i)) .EQN 3 -44 0 0 (vo)[(i)=?(m)/(sec) .EQN 0 22 0 0 (vf)[(i)=?(m)/(sec) .EQN 0 22 0 0 ({0:\Dt}NAME)[(i)=?sec .TXT 5 -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 15 0 0 wT(b):(u((wo)[(i))+(ao)[(i)*b)/(\(1+(((u((wo)[(i))+(ao)[(i)*b)/(c)))^(2))) .EQN 0 26 0 0 x(b):({0:\g}NAME(wT(b))-{0:\g}NAME((wo)[(i)))*((c)^(2))/((ao)[(i)) .EQN 9 -17 0 0 vT(b):v(wT(b)) .EQN 0 17 0 0 t(b):Dt((ao)[(i),wT(b),(wo)[(i),x(b),b) .EQN 4 -17 0 0 uT(b):u(wT(b)) .EQN 0 17 0 0 {0:\t}NAME(b):{0:D\t}NAME((ao)[(i),wT(b),(wo)[(i),x(b),b) .EQN 5 -12 0 0 bInc:(({0:\Db}NAME)[(i))/(100) .EQN 0 12 0 0 b:0*sec,bInc;({0:\Db}NAME)[(i) .EQN 4 -41 0 0 &&b,t(b),{0:\t}NAME(b)@&&x(b) 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 23 17 .EQN 0 37 0 0 &&wT(b),vT(b),uT(b)@&&x(b) 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 22 17 .EQN 23 -37 0 0 &&b,t(b),{0:\t}NAME(b)@&&b 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 23 17 .EQN 1 37 0 0 &&wT(b),vT(b),uT(b)@&&b 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 22 17 .TXT 25 -37 0 0 C x1,1,0,0 .TXT 5 1 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 a52.375000,72.000000,78 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {Inertial Relativistic (Non-Accelerated Observer)}{ Velocities/Elapsed-Time:}} } .EQN 4 0 0 0 (wo)[(k)=?c .EQN 0 22 0 0 (wf)[(k)=?c .EQN 0 22 0 0 ({0:\Db}NAME)[(k)=?iyr .TXT 4 -44 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 3 0 0 0 (uo)[(k):u((wo)[(k)) .EQN 0 22 0 0 (uf)[(k):u((wf)[(k)) .EQN 0 22 0 0 ({0:\D\t}NAME)[(k):{0:D\t}NAME((ao)[(i),(wf)[(k),(wo)[(k),({0:\Dx}NAME)[(i),({0:\Db}NAME)[(k)) .EQN 3 -44 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 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((wo)[(k)) .EQN 0 22 0 0 (vf)[(k):v((wf)[(k)) .EQN 0 22 0 0 ({0:\Dt}NAME)[(k):Dt((ao)[(i),(wf)[(k),(wo)[(k),({0:\Dx}NAME)[(i),({0:\Db}NAME)[(k)) .EQN 3 -44 0 0 (vo)[(k)=?(m)/(sec) .EQN 0 22 0 0 (vf)[(k)=?(m)/(sec) .EQN 0 22 0 0 ({0:\Dt}NAME)[(k)=?sec .TXT 4 -45 0 0 Cg a40.500000,73.000000,51 {\rtf1\ansi \deff0 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Symbol;} } {\plain {\f0 \fs28 Some Graphs of the Alternate Solution:}} } .EQN 6 15 0 0 wT(b):(u((wo)[(k))+(ao)[(i)*b)/(\(1+(((u((wo)[(k))+(ao)[(i)*b)/(c)))^(2))) .EQN 0 26 0 0 x(b):({0:\g}NAME(wT(b))-{0:\g}NAME((wo)[(k)))*((c)^(2))/((ao)[(i)) .EQN 9 -17 0 0 vT(b):v(wT(b)) .EQN 0 17 0 0 t(b):Dt((ao)[(i),wT(b),(wo)[(k),x(b),b) .EQN 3 -17 0 0 uT(b):u(wT(b)) .EQN 0 17 0 0 {0:\t}NAME(b):{0:D\t}NAME((ao)[(i),wT(b),(wo)[(k),x(b),b) .EQN 5 -12 0 0 bInc:(({0:\Db}NAME)[(k))/(100) .EQN 0 12 0 0 b:0*sec,bInc;({0:\Db}NAME)[(k) .EQN 4 -41 0 0 _n_u_l_l_&_n_u_l_l_&b,t(b),{0:\t}NAME(b)@_n_u_l_l_&_n_u_l_l_&x(b) 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 23 17 .EQN 0 37 0 0 _n_u_l_l_&_n_u_l_l_&wT(b),vT(b),uT(b)@_n_u_l_l_&_n_u_l_l_&x(b) 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 22 17 .EQN 23 -37 0 0 _n_u_l_l_&_n_u_l_l_&b,t(b),{0:\t}NAME(b)@_n_u_l_l_&_n_u_l_l_&b 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 23 17 .EQN 1 37 0 0 _n_u_l_l_&_n_u_l_l_&wT(b),vT(b),uT(b)@_n_u_l_l_&_n_u_l_l_&b 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 22 17