desc: Mambo column description

s1, ..., sn: variable names

The function CoeffExtract returns a Mambo description with number of rows equal to the number of rows of its first argument and number of columns equal to the number of variable names.

The (i,j)-th element of the output equals the coefficient of the j-th variable in the i-th row of the first argument.

Restart;
DeclareObservers[A];
DeclarePoints[A,P];
DeclareTriads[a];
DefineObservers[A,A,a];
DefinePoints[A,P,a,q1,q2,q3];
DeclareStates[q1,q2,q3];
kde=Union[{DiffTime[q1^2+q2^2+q3^2]==0},{q1'==u1,q2'==u2}];
kde=Solve[kde,Table[Symbol["q"<>ToString[i]]',{i,3}]]//Flatten;
vel=VelocityDescription[{LinearVelocity[A,P]/.kde}]

$\left\{''Type''\to ''Description'',''Size''\to \left\{1,1\right\},\left\{1,1\right\}\to \left\{''Type''\to ''Vector'',''Size''\to 1,1\to \left\{''Coordinates''\to \left\{\mathrm{u1},\mathrm{u2},-\frac{\mathrm{q1}\mathrm{u1}+\mathrm{q2}\mathrm{u2}}{\mathrm{q3}}\right\},''Triad''\to a\right\}\right\}\right\}$

CoeffExtract[vel,{u1, u2}]

$\left\{''Type''\to ''Description'',''Size''\to \left\{1,2\right\},\left\{1,1\right\}\to \left\{''Type''\to ''Vector'',''Size''\to 1,1\to \left\{''Coordinates''\to \left\{1,0,-\frac{\mathrm{q1}}{\mathrm{q3}}\right\},''Triad''\to a\right\}\right\},\left\{1,2\right\}\to \left\{''Type''\to ''Vector'',''Size''\to 1,1\to \left\{''Coordinates''\to \left\{0,1,-\frac{\mathrm{q2}}{\mathrm{q3}}\right\},''Triad''\to a\right\}\right\}\right\}$