TENSOR-VALUED FUNCTIONS IN ATTITUDE KINEMATICS AND ORBITAL DYNAMICS

Vladimir Martinusi

Post-Doctoral Fellow
Faculty of Aerospace Engineering and Asher Space Research Institute

This presentation deals with some fundamental problems in rigid body dynamics as well as in astrodynamics and celestial mechanics, with the help of a very useful tool: the tensor algebra. Attitude kinematics and the relative orbital motion problem are two important situations where the use of the tensor instrument simplifies the underlying dynamics while offering new perspectives. A general solution to the attitude-kinematics equation is determined and is expressed as a product of a maximum of three explicitly computable tensor exponentials. An application is presented for the situation wherein the angular velocity has variable magnitude along a uniformly precessing direction, with explicit matrix equations for the rotational state.
Another tensor instrument is presented in order to transform the relative orbital motion problem into the classical Kepler problem. Remarkably, a tensorial regularization of the relative orbital motion problem transforms it into the equation of a harmonic oscillator. In the end, a parallelism among the tensor/quaternion/spinor approaches of dynamics is pointed out.

Monday 31^st May, 2010 at 13:30
Seminar Room, Asher Space Research Institute
Light refreshments will be served before the seminar.