What is the relationship between the principal axis and the axis momenta?

[DingXin998]

I am using Meshlab "filters">>"Quality measure and computations">>"compute geometric measures",I want to know the correponse between principal axis and axis momenta:Principal axes are :

| -0.646643 0.738924 -0.189325 |

| -0.594063 -0.332158 0.732639 |

| -0.478479 -0.586227 -0.653755 |

axis momenta are :

| 21090372.000000 25571990.000000 28672450.000000 |

1）Does 21090372.000000 correspond to |-0.646643 0.738924 -0.189325| in the first row?
2）What is the principle of calculating the principal axis and axis momenta?

The version is V2023.12

[rmathar]

The components of the principal axes are printed between the bars, which means the x, y, z components of the first axis are -0.646643 0.738924 -0.189325, for example. The axis momenta are the eigenvalues of the inertia tensor. The eigenvalue for the axis -0.646643 0.738924 -0.189325 is 21090372 in this example. The inertia tensor is the usual symmetric quadratic form of the distances measured in a coordinate system centered at the center of mass, see https://en.wikipedia.org/wiki/Moment_of_inertia .