EOM_SLIP_paw_pad.txt

kill(all);

depends([xl,xf,phi],t);

dxl:diff(xl,t);
dxf:diff(xf,t);
dphi:diff(phi,t);
ddxl:diff(xl,t,2);
ddxf:diff(xf,t,2);
ddphi:diff(phi,t,2);


q:[xl,xf,phi];
dq:[dxl,dxf,dphi];
ddq:[ddxl,ddxf,ddphi];

f:[fl,ff,0];

ll:xl+ll0;
lf:xf+lf0;

lall:ll+lf;


dll:diff(ll,t);
dlf:diff(lf,t);
dlall:diff(lall,t);

x:lall*cos(phi);
y:lall*sin(phi);
xf:lf*cos(phi);
yf:lf*sin(phi);
dx:diff(x,t);
dy:diff(y,t);
dxf:diff(xf,t);
dyf:diff(yf,t);


v:trigsimp(sqrt(dx^2+dy^2));
vf:trigsimp(sqrt(dxf^2+dyf^2));

v:trigsimp(sqrt(dlall^2 +lall^2*dphi^2));
vf:trigsimp(sqrt(dlf^2 +lf^2*dphi^2));

K:1/2*(1-a)*m*v^2 +1/2*a*m*vf^2;
U:(1-a)*m*g*y +a*m*g*yf +1/2*kl*xl^2 +1/2*kf*xf^2;
D:1/2*df*vf^2;

L:K-U;

N:length(q);
for i:1 step 1 thru N do (
dLq[i]:diff(L,dq[i]),
temp:0,
for j:1 step 1 thru N do (
        temp:temp + diff(dLq[i],dq[j])*ddq[j]
            + diff(dLq[i],q[j])*dq[j]),
ddLq[i]:temp,
eq[i]:ddLq[i] - diff(L,q[i]) + diff(D,dq[i]) - f[i]);

for i:1 thru N do
    print(eq[i]);