Concatenate Finite Rotations

Lest take for instance a direct example from Allan Cox' book Plate Tectonics: How it works for the motion of the Australian plate with respect to the Antarctic plate. We are provided with total finite rotations (Table 7-3) for the ages 37 and 42 Ma (mega-annun, meaning million years before present):

However, we wish the Finite Rotation for the age of 40 Ma, requiring us to interpolate:

using PlateKinematics
using PlateKinematics: FiniteRotSph, Covariance
using PlateKinematics: Interpolate_FiniteRotation

FRs_37 = FiniteRotSph(34.4, 11.9, -20.5, 37.0);
FRs_42 = FiniteRotSph(34.8, 10.3, -23.6, 42.0);
Interpolate_FiniteRotation(FRs_37, FRs_42, 40.0)

The output finite rotation will be something in the lines of:

FiniteRotSph:
        Lon     : -145.35
        Lat     : -10.89
        Angle   : 22.36
        Time    : 40.0
        Covariance : Covariance(0.0, 0.0, 0.0, 0.0, 0.0, 0.0)

Similarly, one may interpolate between one finite rotation and present-day, shall we lack a younger constrain for the desired motion. For instance, we may wish interpolate the motion of the Australian plate at 30 Ma:

Interpolate_FiniteRotation(FRs_37, 30.0)

FiniteRotSph:
        Lon        : -145.6
        Lat        : -11.9
        Angle      : 16.62
        Time       : 30.0
        Covariance : Covariance(0.0, 0.0, 0.0, 0.0, 0.0, 0.0)

For such cases, the Euler Pole will remain the same, but the angle will be linearly interpolated.