Body

    <one_body> ::=
        (scalar) <mass> , 
        (Vec3)   <relative_center_of_mass> ,
        (Mat3x3) <inertia_matrix>
        [ , inertial , 
            { node | (OrientationMatrix) <orientation_matrix> } ]

    <normal_arglist> ::= <node_label> ,
        { <one_body>
        | condense, (integer) <num_masses> ,
            <one_body> [ , ... ] }

If only one mass is defined, the first method should be used. Otherwise, many masses can be referred to the same element by means of the keyword condense, followed by the number of expected masses num_masses. The format of each sub-mass is the same as for the single mass input (actually, when condense is not supplied, num_masses is assumed to be 1).

The inertia_matrix is always referred to the center of mass of the mass that is being added. It can be rotated locally by means of the extra orientation_matrix supplied after the (optional) keyword inertial. The keyword node corresponds to the default, i.e. the inertia matrix is assumed to be input in the node reference frame.

Note: in many commercial finite element software, the off-diagonal elements of the inertia matrix are defined with a minus sign; for instance, NASTRAN's CONM2 lumped inertia card expects the values as indicated in Figure 8.6.

Figure 8.6: NASTRAN CONM2 card

$.......2.......3.......4.......5.......6.......7.......8.......
CONM2   EID     G       CID     M       X1      X2      X3
        I11     I21     I22     I31     I32     I33

However, the matrix is reconstructed as

NASTRAN  : : = $$\left[\vphantom{ \begin{array}{ cccccc } M & & & & & \\ & M ... ... & \\ & & & -I21 & I22 & \\ & & & -I31 & -I32 & I33 \end{array} }\right.$$$$\begin{array}{ cccccc } M & & & & & \\ & M & & \multicolumn{... ...& & I11 & & \\ & & & -I21 & I22 & \\ & & & -I31 & -I32 & I33 \end{array}$$$$\left.\vphantom{ \begin{array}{ cccccc } M & & & & & \\ & M ... ... & \\ & & & -I21 & I22 & \\ & & & -I31 & -I32 & I33 \end{array} }\right]$$

see for instance NASTRAN V70.5 Quick Reference Guide for details.

On the contrary, MBDyn directly reads the matrix that will be used in the computation, i.e. without the minus signs in the off-diagonal terms, as reported below:

MBDyn  : : = $$\left[\vphantom{ \begin{array}{ ccc } i11 & i12 & i13 \\ & i22 & i23 \\ \multicolumn{2}{l}{\mathrm{sym.}} & i33 \end{array} }\right.$$$$\begin{array}{ ccc } i11 & i12 & i13 \\ & i22 & i23 \\ \multicolumn{2}{l}{\mathrm{sym.}} & i33 \end{array}$$$$\left.\vphantom{ \begin{array}{ ccc } i11 & i12 & i13 \\ & i22 & i23 \\ \multicolumn{2}{l}{\mathrm{sym.}} & i33 \end{array} }\right]$$

So:

i11 = I11

i22 = I22

i33 = I33

i12 = - I21

i13 = - I31

i23 = - I32

The inertia properties of the model can be logged and verified by means of the inertia keyword, as detailed in Section 8.22.2.

Example.

    set: integer NODE_LABEL = 100;
    set: integer BODY_LABEL = 100;

    # single mass example
    body: BODY_LABEL, NODE_LABEL,
        8.,                            # mass
        reference, node, 0., 0., 0.,   # c.m. offset
        diag, 4.8, 4.8, .4;            # inertia tensor

    # three masses example (equivalent to the previous one)
    body: BODY_LABEL, NODE_LABEL,
        condense, 3,
        4.,                            # mass 1 (mid)
        reference, node, 0., 0., 0.,   # c.m. offset 1
        diag, .4, .4, .2,              # inertia tensor 1
        2.,                            # mass 2 (top)
        reference, node, 0., 0., 1.,   # c.m. offset 2
        diag, .2, .2, .1,              # inertia tensor 2
        2.,                            # mass 3 (bottom)
        reference, node, 0., 0., -1.,  # c.m. offset 3
        diag, .2, .2, .1;              # inertia tensor 3