Introduce motion constraints corresponding to
- The rolling-without-slipping constraint;
- The constraint that the contact between the tire and the surface of the horizontal plane be tangential; and
- The constraint that the instantaneous contact points coincide.
In the MAMBO toolbox, type
>DeclareStates(q1,q2,q3,q4,q5,q6,q7,q8,q9,q10);
>mconst1:={seq((LinearVelocity(W,B) &++ (AngularVelocity(w,b) &xx FindTranslation(B,P1))) &oo cat(w,k)=0,k=1..3)};
>mconst2:=DiffTime({seq(FindTranslation(P1,P2) &oo cat(w,k),k=1..2)});
>mconst3:=DiffTime({w3 &oo MakeTranslations(b,-R*(1+1/20*cos(q8))*sin(q7),R*(1+1/20*cos(q8))*cos(q7),0),w3 &oo MakeTranslations(b,-R/20*sin(q8)*cos(q7),-R/20*sin(q8)*sin(q7),R/20*cos(q8))});
Introduce independent velocity coordinates and formulate the corresponding kinematic differential equations.
In the MAMBO toolbox, type >kde:=mconst1 union mconst2 union mconst3 union {q4t=u1,q5t=u2,q6t=u3};
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