I am trying to manipulate some equations of motion in block matrix form. My first attempt is with the old linalg package because I don't want the submatrices to expand until I am ready However, linalg is not working as I expected. In particular, the formation of EoM1 in the eample below does not lead the &* operator propagating into a block matrix multiplication. If there is a better way to do this with the Linear Algebra package, I would sure like to see an example. Failing that, what am I doing wrong in the linalg example? The example is a linear case. I also will be trying to do nonlinear cases involving multiple block matrix multiplications. The example below is in the old text ouput (edited for clarity). I have been unable to get worksheets to upload successfully into MaplePrimes. Any help will be greatly appreciated.

Thanks,

Neill Smith

# Equations of motion in matrix form in linalg package.

> restart;

> with(linalg);

# Define*simple*matrices and vectors;

> TAM := matrix(3, 3, [Xud, 0, 0, 0, Yvd, 0, 0, 0, Zwd]);

                                  [Xud   0    0 ]

                           TAM := [ 0   Yvd   0 ]

                                  [ 0    0   Zwd]

> TRAM := matrix(3, 3, [0, Xqd, 0, Ypd, 0, Yrd, 0, Zqd, 0]);

                                   [ 0   Xqd   0 ]

                           TRAM := [Ypd   0   Yrd]

                                   [ 0   Zqd   0 ]

> RAM := matrix(3, 3, [Kpd, 0, Krd, 0, Mqd, 0, Npd, 0, Nrd]);

                                  [Kpd   0   Krd]

                           RAM := [ 0   Mqd   0 ]

                                  [Npd   0   Nrd]

> RTAM := matrix(3, 3, [0, Kvd, 0, Mud, 0, Mwd, 0, Nvd, 0]);

                                   [ 0   Kvd   0 ]

                           RTAM := [Mud   0   Mwd]

                                   [ 0   Nvd   0 ]

> Vel := matrix(3, 1, [u, v, w]);

                                        [u]

                                 Vel := [v]

                                        [w]

> Omg := matrix(3, 1, [p, q, r]);

                                        [p]

                                 Omg := [q]

                                        [r]

# Create matrix EoM by 1st method

> MAM := matrix(2, 2, ['TAM', 'TRAM', 'RTAM', 'RAM']);

                                    [TAM   TRAM]

                                    [RTAM  RAM ]

> MAM;

                                     MAM

> evalm(MAM);

                                [TAM   TRAM]

                                [RTAM  RAM ]

> S := matrix(2, 1, ['Vel', 'Omg']);

                                      [Vel]

                                 S := [   ]

                                      [Omg]

> S;

                                      S

> evalm(S);

                                    [Vel]

                                    [Omg]

> EoM := `&*`(MAM, S);

                               EoM := MAM &* S

> EoM;

                                  MAM &* S

> EoM1 := evalm(EoM);

                                [TAM Vel + TRAM Omg]

                                [RTAM Vel + RAM Omg]

# However, note that the &* operator did not "propagate" inside of the definition of matrix EoM1.

> EoM1;

                                    EoM1

> evalm(EoM1);

                            [TAM Vel + TRAM Omg]

                            [RTAM Vel + RAM Omg]

> evalm(EoM1[1]);

Error, array defined with 2 indices, used with 1 indices

> evalm(EoM1[1, 1]);

Error, (in evalm/evaluate) use the &* operator for matrix/vector multiplication

# As noted above the &* operator did not "propagate" inside of the definition of matrix EoM1.

# What we would really like to get would be

> EoM2 := matrix(2, 1, [`&*`('TAM', 'Vel')+`&*`('TRAM', 'Omg'), `&*`('RTAM', 'Vel')+`&*`('RAM', 'Omg')]);

                             [TAM &* Vel + TRAM &* Omg]

                     EoM2 := [                        ]

                             [RTAM &* Vel + RAM &* Omg]

# This looks like EoM1 except that the &* operator is now inside the definition of EoM2.

> EoM2[1, 1];

                          TAM &* Vel + TRAM &* Omg

> evalm(EoM2);

                         [TAM &* Vel + TRAM &* Omg]

                         [RTAM &* Vel + RAM &* Omg]

> evalm(EoM2[1, 1]);

                           [    Xud u + Xqd q    ]

                           [Yvd v + Ypd p + Yrd r]

                           [    Zwd w + Zqd q    ]

> evalm(EoM2[2, 1]);

                           [Kvd v + Kpd p + Krd r]

                           [Mud u + Mwd w + Mqd q]

                           [Nvd v + Npd p + Nrd r]

> evalm(EoM2[1, 1])[1, 1];

                                Xud u + Xqd q

# # Create matrix EoM by 3rd method

> MAM := blockmatrix(2, 2, [TAM, TRAM, RTAM, RAM]);

                           [Xud   0    0    0   Xqd   0 ]

                           [ 0   Yvd   0   Ypd   0   Yrd]

                           [ 0    0   Zwd   0   Zqd   0 ]

                    MAM := [                            ]

                           [ 0   Kvd   0   Kpd   0   Krd]

                           [Mud   0   Mwd   0   Mqd   0 ]

                           [ 0   Nvd   0   Npd   0   Nrd]

> MAM;

                                     MAM

> evalm(MAM);

                       [Xud   0    0    0   Xqd   0 ]

                       [ 0   Yvd   0   Ypd   0   Yrd]

                       [ 0    0   Zwd   0   Zqd   0 ]

                       [ 0   Kvd   0   Kpd   0   Krd]

                       [Mud   0   Mwd   0   Mqd   0 ]

                       [ 0   Nvd   0   Npd   0   Nrd]

> S := stackmatrix(Vel, Omg);

                                       [u]

                                       [v]

                                       [w]

                                  S := [ ]

                                       [p]

                                       [q]

                                       [r]

> EoM3 := `&*`(MAM, S);

                              EoM3 := MAM &* S

> EoM3;

                                  MAM &* S

> evalm(EoM3);

                           [    Xud u + Xqd q    ]

                           [Yvd v + Ypd p + Yrd r]

                           [    Zwd w + Zqd q    ]

                           [Kvd v + Kpd p + Krd r]

                           [Mud u + Mwd w + Mqd q]

                           [Nvd v + Npd p + Nrd r]

>