Frame 11

Proceed to derive the dynamic equations of motion of the wheel with gravity as the only applied force.

In the MAMBO toolbox, type

>kde:=solve(kde,{q1t,q2t,q3t,q4t,q5t,q6t,q7t,q8t,q9t,q10t});
>v:=subs(kde,VelocityDescription([LinearVelocity(W,B),AngularVelocity(w,b)]));
>beta:=CoeffExtract(v,[u1,u2,u3]);
>p:=subs(kde,MomentumDescription([LinearMomentum(W,B,m),AngularMomentum(W,b,matrix([[m*R^2/2,0,0],[0,m*R^2/2,0],[0,0,m*R^2]]))]));
>force:=ForceDescription([MakeTranslations(w,0,0,-m*g),NullVector()]);
>DeclareStates(u1,u2,u3);
>dde:=convert((subs(kde,DiffTime(p,w)) &-- force) &oo beta,set);

(Note that the 'VelocityDescription', 'CoeffExtract', 'MomentumDescription', and 'ForceDescription' functions are only available with the MAMBO toolbox 2.0.)

Use the MAMBO toolbox to generate a corresponding MAMBO motion description.

In the MAMBO toolbox, type

>MotionOutput(ode=kde union dde,filename="c:\\MamboProjects/tutorial.dyn",parameters=[m=1,g=10,thickness=0.01,length=10,width=10,R=1,marker=.02],states=[u1=0,u2=-3,u3=3,q1=0,q2=0,q4=0.3,q5=0.7,q6=1.7,q7=3.012388980,q3=0.6942176872,q8=5.412388980,q9=0.2260263213,q10=-0.7306816499]);

Reload the motion description into the MAMBO project by selecting the 'File->Reload Simulation' menu item. Generate a time history corresponding to the initial values for the MAMBO state variables and animate the result.

Frame 11