Rotation and tumbling

Fixed-axis spin

The body turns by 2π t / P about an axis fixed in the body frame (given by its azimuth from +X toward +Y and its elevation toward +Z), after the attitude law and the Euler angles.

Free tumbling

A body spinning about an axis that is not a principal axis of inertia does not keep that axis: it precesses and nutates, and its light curve is not strictly periodic. LightCurve integrates Euler’s torque-free equations:

I · dω/dt = −ω × (I · ω)          (body frame, principal axes = body axes)
dq/dt     = ½ q ⊗ (0, ω)          (attitude quaternion)

with a fixed-step fourth-order Runge–Kutta scheme, quaternions interpolated spherically between steps, and states cached. Energy and angular momentum are conserved to the integration accuracy (tested); a spin about the major axis stays stable, a spin about the intermediate axis flips.

Inputs: the three principal moments of inertia (relative; they can be estimated from the bounding box of the model, taken as a full homogeneous box), the initial axis and the initial period.