GraphingCalculator 4;
Window 44 0 859 1440;
PaneDivider 446;
SignificantDigits 10;
FontSizes 18;
BackgroundType 0;
StackPanes 1;
SliderControlValue 0;
2D.Scale 0.5 0.5 2 2;
2D.BottomLeft -0.90625 -0.96875;
2D.Axes 0;
2D.GraphPaper 0;
Text "Motion diagrams for flight of a projectile and other sample accelerations.

Version 0.55   9-4-14

A = launch angle; V_0 = initial velocity; V_X,Y = x,y components of initial velocity; X,Y_0 = initial position; m= mass; g = vertical acceleration (gravitation for g=1);  G,H,M (horizontal) and g,K,L (vertical) are quadratic, cubic, and quartic ""accelerations"".   (G=H=M=K=L=0 and g=1 is conventional projectile motion.)  

Good starting values for projectile motion are a=0.425 and V0=6.5.   
The ""hook"" set: a=0.875; V0=6.15; m=1; g=1; G=-1; M=K=L=0; s=6.25; N=19; f=1; k=-0.5; l=0.5.";
Color 2;
MathPaneSlider 35;
Expr a=slider([0,1,40]);
Color 17;
Expr A;
MathPaneSlider 123;
Expr V_0=slider([0,10]);
Color 6;
Expr A=pi/2*a;
Color 5;
Expr V_X=V_0*cos(A),V_Y=V_0*sin(A);
Color 3;
Expr X_0=0,Y_0=0;
Expr m=1;
Color 4;
MathPaneSlider 40;
Expr g=slider([-1,1,40]);
Color 6;
Expr G=slider([-1,1,40]);
Color 7;
MathPaneSlider 28;
Expr H=slider([-1,1,40]);
Color 3;
MathPaneSlider 20;
Expr M=slider([-1,1,40]);
MathPaneSlider 20;
Expr K=slider([-1,1,40]);
Color 4;
MathPaneSlider 20;
Expr L=slider([-1,1,40]);
Text "Position, velocity, and force (acceleration):";
Color 2;
Expr function(X,T)=vector(X_0+V_X*T+1/2*G*T^2+1/6*H*T^3+1/24*M*T^4,Y_0+V_Y*T-(1/2*g*T^2)+1/6*K*T^3+1/24*L*T^4);
Color 8;
Expr function(V,T)=vector(V_X+G*n+1/2*H*n^2+1/6*M*T^3,V_Y-(g*n)+1/2*K*n^2+1/6*L*T^3);
Expr function(F,T)=vector(G+H*n+1/2*M*T^2,-g+K*n+1/2*L*T^2)*m;
Color 7;
Expr O=vector(0,0),I=vector(1,0),J=vector(0,1);
Text "For circular motion (swap X with Y) [experimental – acceleration differences freak out; component calculations do not include this case]:";
Color 5;
Expr R=5;
Color 4;
Expr function(Y,T)=vector(R*cos([V_0*T]),R*sin([V_0*T]));
Text "Origin:";
Color 17;
Expr O;
Text "Object and its path:";
Color 8;
Expr function(X,n);
Color 17;
Expr function(X,t*n);
Color 17;
Expr function(X,10*t);
Text "Position vector:";
Color 17;
Expr O,function(X,n);
Text "x and y components of position:";
Color 17;
Expr O,I*[dot(I,function(X,n))];
Color 17;
Expr O,J*[dot(J,function(X,n))];
Text "Velocity vector:";
Color 17;
Expr function(X,n),function(X,n)+function(V,n);
Text "x and y components of velocity:";
Color 17;
Expr function(X,n),function(X,n)+I*[dot(I,function(V,n))];
Color 17;
Expr function(X,n),function(X,n)+J*[dot(J,function(V,n))];
Text "Force (acceleration) vector:";
Color 17;
Expr function(X,n),function(X,n)+function(F,n);
Text "Tangential (parallel) and perpendicular components of the force (acceleration):";
Color 2;
Expr function(F_(p*a*r),n)=function(V,n)*[dot(function(F,n),function(V,n))]/dot(function(V,n),function(V,n));
Color 17;
Expr function(X,n),function(X,n)+function(F_(p*a*r),n);
Color 17;
Expr function(X,n),function(X,n)+function(F,n)-function(F_(p*a*r),n);
Text "Motion Diagram.  S= total time to track; N = number of steps; d = time step.   Displacement.  (Divide by d to get velocity.)   Acceleration.   
f=scale factor; k,l, E horizontal and vertical offset (for visibility)";
Color 8;
MathPaneSlider 125;
Expr S=slider([0,10]);
Color 4;
MathPaneSlider 19;
Expr N=slider([0,30,30]);
Color 5;
Expr d=S/N;
Color 8;
Expr f=slider([1,5]);
Color 2;
Expr k=slider([-0.5,0.5,40]);
Color 6;
MathPaneSlider 40;
Expr l=slider([-0.5,0.5,40]);
Color 3;
Expr E=vector(k,l);
Text "Position vectors at adjustable snapshot values and corresponding displacement vector:";
Color 5;
MathPaneSlider 14;
Expr p=slider([0,30,30]);
Color 6;
MathPaneSlider 20;
Expr q=slider([0,30,30]);
Color 17;
Expr O,function(X,p*d);
Color 17;
Expr function(X,p*d);
Color 17;
Expr O,function(X,q*d);
Color 17;
Expr function(X,q*d);
Color 17;
Expr function(X,q*d),function(X,p*d);
Text "Points at evenly spaced moments of time:";
Color 17;
Expr function(X,a*d),a=set(0*ldots*30);
Text "Displacement vectors:";
Color 17;
Expr function(X,a*d),function(X,[a+1]*d),a=set(0*ldots*30);
Text "Velocity vectors:";
Color 17;
Expr function(X,a*d),(function(X,[a+1]*d)-function(X,a*d))/d+function(X,a*d),a=set(0*ldots*30);
Text "Acceleration vectors.   f is a scale factor and E is an offset (both for visibility) .";
Color 17;
Expr function(X,[a+1]*d)+E,[function(X,[a+2]*d)+function(X,a*d)-(function(X,[a+1]*d)*2)]/d^2*f+function(X,[a+1]*d)+E,a=set(0*ldots*30);
Text "<size=16>
Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";