int main(int argc, char *argv[]){
try{
SX a("a"),b("b"),c("c");
SX x("x"),y("y"),z("z");
SXMatrix u=14;
SX da("da"),db("db"),dc("dc");
SX dx("dx"),dy("dy"),dz("dz");
SX dda("dda"),ddb("ddb"),ddc("ddc");
SX ddx("ddx"),ddy("ddy"),ddz("ddz");
SXMatrix q;q << a << b << c << x << y << z;
SXMatrix dq;dq << da << db << dc << dx << dy << dz;
SXMatrix ddq;ddq << dda << ddb << ddc << ddx << ddy << ddz;
Frame f0("World Frame",q,dq,ddq);
Frame f1("f1",f0,TRx(a)*tr(x,0,0)*TRy(b));
Frame f2("f2",f1,tr(0,y,z));
Frame f3("f3",f2,TRz(c));
Frame f4("f4",f3,TRz(u));
//utest("q0",KinVec(a,b,c,0,f0),q,dq,t);utest("q1",KinVec(x,y,z,0,f0),q,dq,t);
//utest("dq0",KinVec(da,db,dc,0,f0),q,dq,t);utest("dq1",KinVec(dx,dy,dz,0,f0),q,dq,t);
//utest("ddq0",KinVec(da.der(t),db.der(t),dc.der(t),0,f0),q,dq,t);utest("ddq1",KinVec(dx.der(t),dy.der(t),dz.der(t),0,f0),q,dq,t);
KinVec v = pos( f3, f0 );
utest("p303",v.expressedIn(f3),q,dq,ddq);
v = vel( f3, f0, f0, q, dq, ddq );
utest("v300",v,q,dq,ddq);
utest("v301",vel(f3,f0,f1),q,dq,ddq);
utest("a100",acc(f1,f0,f0),q,dq,ddq);
//cout << acc(f1,f0,f0) << endl;
utest("a300",acc(f3,f0,f0),q,dq,ddq);
utest("a301",acc(f3,f0,f1),q,dq,ddq);
KinVec w=rotVel(f1,f0,f0);
utest("w100",w,q,dq,ddq);
utest("w300",rotVel(f3,f0,f0),q,dq,ddq);
utest("w103",rotVel(f1,f0,f3),q,dq,ddq);
utest("alph103",rotAcc(f1,f0,f3),q,dq,ddq);
// Operations on KinVecs
KinVec A=rotVel(f1,f0,f0)+rotVel(f2,f1,f0)+rotVel(f3,f2,f0);
KinVec B=rotVel(f3,f0,f0); // a-c is zero (relation from mechanics)
KinVec C=rotVel(f3,f0,f1); // b-c is zero
utest("A",A,q,dq,ddq);
utest("0",A-B,q,dq,ddq);
utest("0",A-C,q,dq,ddq);
utest("0",cross(A,B*2),q,dq,ddq); // parallel vectors have zero crossproduct
KinVec x0(1,0,0,0,f0);
KinVec x1(0,1,0,0,f0);
utest("0",cross(x0,x1)-ez(f0),q,dq,ddq); // (1,0,0) ^ (0,1,0) = (0,0,1)
utest("A",A,q,dq,ddq);
A[2]=3.14;
utest("A3.14",A,q,dq,ddq);
// raw constructors
KinVec x2(a,b,c,0,f0);
KinVec x3(da,db,dc,0,f0);
//KinVec x4=x2.der();
utest("0",x2.der()-x3,q,dq,ddq);
// Mixed Datatypes
SXMatrix c0=a;
SXMatrix c1=b;
KinVec x4(c0,c1,c,0,f0);
utest("0",x4.der()-x3,q,dq,ddq);
KinVec a0=acc(f4,f0,f0);
//
SXMatrix phi("phi"),theta("theta"),delta("delta"); // The states we will use
SXMatrix dphi("dphi"),dtheta("dtheta"),ddelta("ddelta");
SXMatrix ddphi("ddphi"),ddtheta("ddtheta"),dddelta("dddelta");
SXMatrix q_; q_<< phi << theta << delta; // The time changing variables of our system
SXMatrix dq_; dq_<< dphi << dtheta << ddelta; // The derivatives of these variables
SXMatrix ddq_; ddq_<< ddphi << ddtheta << dddelta;
SXMatrix r("r");
Frame F0("world frame",q_,dq_,ddq_);
Frame F1("CM frame",F0,TRz(phi)*TRy(-theta)*tr(a,0,0));
Frame F2("rotating frame",F1,TRx(delta));
return 0;
} catch (const char * str){
cerr << str << endl;
return 1;
}
}
Frame expressCommon(KinVec &a,KinVec &b) {
Frame c=a.ref.getCommonFrame(b.ref);
a=a.expressedIn(c);
b=b.expressedIn(c);
return c;
}