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The Small Gravitational Torque Forced a Rotating Triaxial Body

Kaźmierczak A.

Journal of Applied Computer Science Methods

2011

Vol. 3 No. 2

45--64

In his paper I examine influence of small gravitational torque on rotation of elongated triaxial bodies. The Hamiltonian of a body moving in central gravitational field separates on two parts: orbital movement about central body and a rotation around the body mass center. For the small bodies like asteroids the separation spin-orbit constant has rate 10-12 of total energy and orbital and rotational motion are almost independent. This way we may consider orbital motion as a known function of time or true anomaly. Using the Hamiltonian I found gravitational torque affecting triaxial body in quadruple approximation. The Euler-Liouville equation is a system of non-linear differential equations. Position of the body is described by six variables: vector R in inertial reference system and three Euler angle: φ, ψ and ϑ rigidly bounded to the principal axes of the body inertia tensor. The rotational motion is described by angular velocity (vector ω) or angular momentum vector L=Îω or Î=diag(Ix,Iy,Iz) or Î=Izdiag(a;b;1) denotes diagonal inertia tensor of the body) and three Euler angle. A numerical resolution of gravitationally disturbed Euler- Liouville equation is compared with the undisturbed one. This solution is well known as the Poinset solution of the free body rotation. Modelling of rotational motion is a great interest because its connections to astronomical measurements of asteroids physical properties. I found that direction of spin-vector of a rotating body in NPA state of motion changes markedly when forced by gravitational torque.