GraphingCalculator 4;
Window 45 5 850 1404;
PaneDivider 491;
SignificantDigits 14;
FontSizes 18;
BackgroundType 0;
StackPanes 1;
SliderControlValue 0;
T 0 5;
2D.BottomLeft -1.796875 -2.59375;
2D.Axes 0;
2D.GraphPaper 0;
Text "Reference frames: Lorentzian relativity.
Version 0.3, 2-12-09
To do:
(i) ?

Relative to what?


Speed of light";
Color 5;
MathPaneSlider 4;
Expr c=slider([0,10,40]);
Text "Initial location of observer Q";
Color 4;
MathPaneSlider 149;
Expr a=slider([-1,1]);
Color 3;
MathPaneSlider 147;
Expr b=slider([-1,1]);
Text "Components of velocity of observer Q relative to frame O as fractions of speed of light.   C is speed of Q in O as a fraction of that of light, and T the angle relative to the x-axis. ";
Color 7;
MathPaneSlider 38;
Expr C=slider([0,1,40]);
Color 8;
MathPaneSlider 5;
Expr T=slider([0,2*pi]);
Color 2;
Expr A=C*cos(T);
Color 2;
Expr B=C*sin(T);
Text "Velocity of frame P relative to O as a fraction of the speed of light; rapidity";
Color 5;
MathPaneSlider 37;
Expr f=slider([-1,1,40]);
Color 6;
Expr V=c*f,g=1/sqrt(1-[V/c]^2);
Text "Velocity of frame P relative to O";
Color 4;
Expr W=vector(V,0);
MathPaneSlider 138;
Expr d=slider([0,1]);
Color 6;
MathPaneSlider 49;
Expr h=slider([0,0.1]);
Color 2;
Expr P+J*d,P+J*d+W;
Color 2;
Expr P+J*[d+h],P+J*[d+h]+W;
Text "Basis vectors";
Expr I=vector(1,0),J=vector(0,1);
Text "Origin of frame O; origin of frame P";
Color 3;
Expr O=vector(0,0),P=O+n*W;
Text "Frame with origin O";
Color 17;
Expr O;
Color 3;
Expr O,I;
Color 3;
Expr O,J;
Text "Frame with origin P";
Color 17;
Expr P;
Expr P,P+I;
Expr P,P+J;
Text "Observer Q; velocity of Q relative to frame O";
Color 2;
Expr Q=vector(a,b)+U_O*n,U_O=vector(A,B)*c;
Text "Velocity of Q relative to frame P";
Color 7;
Expr U_P=vector(A-V,B/g)*c/(1-(f*A));
Color 17;
Expr Q;
Text "Velocity of observer Q relative to frame O";
Color 17;
Expr Q,Q+U_O;
Text "Velocity of observer Q relative to frame P (Galilean)";
Color 17;
Expr Q,Q+U_O-W;
Text "Velocity of frame P relative to frame O, planted at Galilean relative velocity of Q";
Color 17;
Expr Q+U_O-W,Q+U_O;
Text "Velocity of observer Q relative to frame P (Lorentzian)";
Color 17;
Expr Q,Q+U_P;
Text "Velocity of frame P relative to frame O, planted at Lorentzian relative velocity of Q";
Color 17;
Expr Q+U_P,Q+U_P+W;
Text "Rod, right isosceles triangle, and circle at rest in frame O";
Color 8;
MathPaneSlider 33;
Expr l=slider([0,0.1]);
Color 4;
Expr D=0.25,E=0.25,m=E/D;
Color 17;
Expr abs(y-b)<l,abs(x-a)<D/2;
Color 17;
Expr 0<y-b<E,abs(x-a)<D/2,y<m*x+b-(m*a)+E/2;
Color 17;
Expr [x-a]^2+[y-b]^2=[D/2]^2;
Text "Lorentz contracted rod, right isosceles triangle, and circle at rest in P";
Color 17;
Expr abs(y-b)<l,abs(x-a-(n*V))<D/(2*g);
Color 17;
Expr 0<y-b<E,abs(x-a-(n*V))<D/(2*g),y<g*m*[x-(n*V)]+b-(g*m*a)+E/2;
Color 17;
Expr g^2*[x-a-(n*V)]^2+[y-b]^2=[D/2]^2;
Text "

<size=14>Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";