The rotation state of a rigid body can be described by the temporal evolution of a coordinate mapping x(ξ, t) from the body frame to the inertial frame at time t with a position vector ξ ∈R3 in the body frame. x is a linear mapping x(ξ, t) = Rξ represented by an orthogonal rotation matrix R(t) ∈R3×3.

Within the body frame, a tensor of inertia JBF ∈R3×3 is prescribed.

The corresponding tensor is J(t) = RJBFR−1 in the inertial frame.

Based on the vectors for the angular velocity, ω(t) ∈R3, for the rotational angular momentum, L(t) ∈R3, and the prescribed torque, T(t) ∈R3, the equations for rotation in the inertial frame are ˙R() = ω × R(), ˙L = T, Jω = L. (1) Together with the initial conditions, R(t0) = R0 and L(t0) = L0, at time t0, this equation poses an initial value problem that determines the temporal evolution of the rotation state, R(t) and L(t).

From the solution of the differential equation, additional variables such as ω, x(ξ, t) are determined.

We take as directions of the inertial frame the J2000 system, with the origin at the center of mass of the cometary body.

Far away from further gravitationally interacting bodies, this translation does not lead to further torques or modifications of Eq. (1).

Within this manuscript all results are based on numerical simulations for the full rotational dynamics.

The equation in the inertial frame has an equivalent representation in the body frame with the Euler equations for rotation, JBF,i j ˙ωBF,j = TBF,i −ϵi jk ωBF,j JBF,kl ωBF,l,
(2)
for variables ωBF = R−1ω and TBF = R−1T.
2.1.

Rigid body geometry Within the body frame with the standard basis vectors, e1, e2, e3 ∈R3, the spatial domain Ω⊂R3 describes the geometrical shape (body shape) of the cometary nucleus.

In the inertial frame at time t the location of the body is the spatial domain Ωt = x(Ω, t).

We consider three idealized body shapes, Ω, complemented by one additional shape, an approximation of the cometary nucleus of comet 67P/C-G.

The first two shapes are ellipsoids and are oriented such that their symmetry axes coincide with e1, e2, e3.

The dimensions of the ellipsoids are characterized by the lengths of the semimajor axis a1 ≥a2 ≥a3 with respect to e1, e2, e3.

The first shape is an oblate ellipsoid with a1 = a2 = 2a3 and is therefore axially symmetric around e3.

An oblate ellipsoid underlies the forced precession models discussed in Whipple & Sekanina (1979) and Sekanina (1984), together with further assumptions on the activity of regional jets on the surface.

The second shape is a near-prolate ellipsoid characterized by 9a1 = 18a2 = 20a3 without axial symmetry.

As a consequence of three different axis lengths this shape is not axially symmetric.

That is why we prefer the denotation near-prolate instead of prolate.

For the numerical study here, we describe the boundaries of Ωfor these two shapes using a surface, ∂Ω, consisting of a triangular mesh with NE = 4000 elements.

The third geometry is given by a bilobed shape and consists of two slightly oblate ellipsoids placed side by side without overlap.

Each ellipsoid satisfies the relation 9a1 = 9a2 = 10a3 such that the bilobed shape holds the same spatial dimensions as the near-prolate ellipsoid.

This bilobed shape configuration could represent a contact binary and is similar to the shape of comet 67P/C-G.

The base vector e1 is located on the line through the centers of the spheres and e2, e3 span the perpendicular plane.

The surface of the domain, Ω, for the bilobed shape consists of NE = 4000 triangular elements.

The last case is a shape model of comet 67P/C-G.

The NE = 3996 surface elements of the last shape are the same as those of Läuter et al. (2022), which are derived from the highresolution (meter-scale) shape model of Preusker et al. (2017).

All shapes share the same normalized volume |Ω| = 18.56 km3.