KeplerPoinsotin

KeplerPoinsotin is a theoretical framework in celestial mechanics that merges Keplerian orbital dynamics with Poinsot's geometric description of rigid-body rotation to model the coupled translational and rotational motion of irregular small bodies in the gravitational field of a primary. The model treats the body’s center of mass as following a Keplerian-like trajectory around a central mass, while its attitude evolves under gravity-gradient torques described in Poinsot’s formulation. This coupling allows simultaneous description of orbital elements and orientation, using variables such as semi-major axis, eccentricity, inclination, Euler angles, and angular velocity, along with the inertia tensor of the body.

In its typical mathematical form, the translational motion is described by Newton's law in a central potential with corrections for non-spherical gravity, and the rotational motion is given by Euler's equations expressed in Poinsot's geometric frame. The gravity gradient torque arises from the deviation of the body's shape from spherical symmetry and couples the two sets of equations. The approach is used primarily in theoretical studies and numerical simulations of small bodies such as elongated asteroids and in planning attitude control for spacecraft operating near irregular bodies.

The term KeplerPoinsotin is attributed to early discussions that sought a unified language for orbital and rotational dynamics around non-spherical primaries. It is not a standard model in mainstream astrodynamics but appears in some pedagogical treatments and exploratory research. Related concepts include the Kepler problem, Poinsot’s top, gravity gradient torque, and rigid-body dynamics.