DYNAMICAL EQUATIONS FOR THE POSITION AND ATTITUDE OF A SPACECRAFT WITH TIME DEPENDENT MASS AND MASS PROPERTIES.
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
Pagination or Media Count:
Nonlinear differential equations for the position and attitude of a spacecraft under the influence of gravitational and nonconservative forces are developed in terms of Lagrangian mechanics. The significance of the results is that the equations are cast in a form which makes them suitable for digital solution. The spacecraft is assumed to have a completely general configuration with mass a function of time, and mass properties a function of time and the generalized coordinates and velocities. The equations of motion for the center of mass of the system are obtained in terms of a perturbation from an arbitrary reference trajectory. The equations describing the attitude motion are in terms of a general set of Euler angles. These angles relate the orientation of a reference frame fixed in the spacecraft to a reference frame whose orientation can be specified as an arbitrary function of time in inertial space. The introduction of a general set of Euler angles provides either for the convenient use of a dual set of angles to avoid singularities or for the selection of a natural set of angles for a specific application. Expressions for the partitioned energies and the generalized forces are also presented. The paper is concluded with the application of the equations of motion for the case when the reference trajectory is a Keplerian ellipse. The effect of the J2 zonal harmonic term of the gravitational potential expansion of the principal gravitating mass and the coupling between the trajectory and attitude motion are included. Author
- Spacecraft Trajectories and Reentry