GraphingCalculator 4;
Window 46 6 856 1440;
PaneDivider 607;
FontSizes 18;
BackgroundType 0;
BackgroundColor 255 255 255;
StackPanes 1;
SliderSteps 400;
SliderControlValue 66;
T -1 1;
U -1 1;
V -1 1;
3D.X -1 1;
3D.Y -1 1;
3D.Z -1 1;
3D.Axes 0;
3D.Depth 2.3330909743;
3D.View 0.6301204552868166 -0.7588649666033165 -0.1645362400671168 0.73810057652866 0.6511686508518501 -0.1765982080316111 0.2411550347003616 -0.01016615040566031 0.970433356098594;
3D.Speed 0;
Text "Precession of a gyroscope, modeled by a simple spinning hoop.

Version 0.25
To do:
(i) Add nutation.
(ii) Add ∆L's due to friction in the hoop and friction in the support.


Basis vectors: rectangular and spherical polar";
Color 4;
Expr I_h=vector(1,0,0),J_h=vector(0,1,0),K_h=vector(0,0,1),O=vector(0,0,0);
Color 4;
Expr function(R_h,T,P)=vector(sin(T)*cos(P),sin(T)*sin(P),cos(T)),function(P_h,T,P)=vector(-sin(P),cos(P),0),function(T_h,T,P)=vector(cos(T)*cos(P),cos(T)*sin(P),-sin(T));
Color 2;
MathPaneSlider 123;
Expr R=slider([0,0.05]);
Text "Acceleration due to gravity";
Color 6;
Expr g=9.800000000000001;
Text "Mass, radius of spinning hoop; length of gyroscope support";
Color 7;
Expr m=0.2,a=0.5;
Color 7;
MathPaneSlider 36;
Expr S=slider([0,5]);
Text "Moment of inertia, angular velocity, and angular momentum of hoop.";
Expr I=m*a^2;
Color 2;
MathPaneSlider 126;
Expr f=slider([-20,20]);
Color 4;
Expr o=2*pi*f;
Color 3;
Expr L=I*o;
Text "Pitch of gyroscope support";
MathPaneSlider 49;
Expr H=slider([0,1,100]);
Color 3;
Expr T=pi*H;
Text "Precession angular frequency";
Color 5;
Expr W=m*g*S*sin([T])/L;
Color 8;
Expr W;
Color 5;
Expr P=W*n;
Text "Angular momentum of hoop (planted at hoop center)";
Color 17;
Expr S*function(R_h,T,P),S*function(R_h,T,P)+L*function(R_h,T,P),'radius'=R;
Color 17;
Expr S*function(R_h,T,2*pi*t)+L*function(R_h,T,2*pi*t);
Text "Gravity";
Color 17;
Expr S*function(R_h,T,P),S*function(R_h,T,P)-(m*g*K_h),'radius'=R;
Text "Lever arm; planted at hoop center";
Color 17;
Expr O,S*function(R_h,T,P),'radius'=R;
Color 17;
Expr S*function(R_h,T,P),2*S*function(R_h,T,P),'radius'=R;
Text "Torque (planted at hoop center)";
Color 2;
Expr function(N,T,P)=cross(S*function(R_h,T,P),[-(m*g*K_h)]);
Color 17;
Expr S*function(R_h,T,P),S*function(R_h,T,P)+function(N,T,P),'radius'=R;
Text "Change in angular momentum ∆L over a time interval d, planted at end of angular momentum; resultant";
Color 3;
MathPaneSlider 82;
Expr d=slider([0,0.5]);
Color 17;
Expr S*function(R_h,T,P)+L*function(R_h,T,P),S*function(R_h,T,P)+L*function(R_h,T,P)+function(N,T,P)*d,'radius'=R;
Color 17;
Expr S*function(R_h,T,P),S*function(R_h,T,P)+L*function(R_h,T,P)+function(N,T,P)*d,'radius'=R;
Color 17;
Expr S*function(R_h,T,P+W*d),S*function(R_h,T,P+W*d)+L*function(R_h,T,P+W*d),'radius'=R;
Text "Stand";
MathPaneSlider 44;
Expr A=slider([0,0.1]);
Color 8;
Expr x^2+y^2=A^2,z<0;
Text "Gyroscope support (same as lever arm planted at fulcrum)";
Color 8;
Grain 1;
Expr O,S*function(R_h,T,P),'radius'=0.03;
Text "The hoop.   Color shading shows rotation of hoop. ";
Color 7;
Grain 1;
Expr S*function(R_h,T,P)+function(P_h,T,P)*u-(function(T_h,T,P)*v),u^2+v^2<a^2,'color'=u*cos([o*n])+v*sin([o*n]);
Color 8;
Grain 1;
Expr S*function(R_h,T,P)+[function(P_h,T,P)*cos([2*pi*t])-(function(T_h,T,P)*sin([2*pi*t]))]*a,'radius'=0.03;
Text "Show rotation of hoop with vectors in plane of hoop.";
Color 5;
MathPaneSlider 88;
Expr s=slider([0,0.05]);
Color 17;
Expr S*function(R_h,T,P),S*function(R_h,T,P)+[function(P_h,T,P)*cos([o*n])-(function(T_h,T,P)*sin([o*n]))]*a,'radius'=s;
Color 17;
Expr S*function(R_h,T,P),S*function(R_h,T,P)-([function(P_h,T,P)*cos([o*n])-(function(T_h,T,P)*sin([o*n]))]*a),'radius'=s;
Color 17;
Expr S*function(R_h,T,P),S*function(R_h,T,P)-([function(P_h,T,P)*sin([o*n])+function(T_h,T,P)*cos([o*n])]*a),'radius'=s;
Color 17;
Expr S*function(R_h,T,P),S*function(R_h,T,P)+[function(P_h,T,P)*sin([o*n])+function(T_h,T,P)*cos([o*n])]*a,'radius'=s;
Text "
<size=15>Author: David A. Craig <<http://web.lemoyne.edu/~craigda>";