A new approach to impulsive rendezvous near circular orbit |
| |
| Authors: | Thomas Carter Mayer Humi |
| |
| Institution: | 1. Professor Emeritus, Department of Mathematics, Eastern Connecticut State University, Willimantic, CT, 06226, USA
2. Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, 01609, USA
|
| |
| Abstract: | A new approach is presented for the problem of planar optimal impulsive rendezvous of a spacecraft in an inertial frame near
a circular orbit in a Newtonian gravitational field. The total characteristic velocity to be minimized is replaced by a related
characteristic-value function and this related optimization problem can be solved in closed form. The solution of this problem
is shown to approach the solution of the original problem in the limit as the boundary conditions approach those of a circular
orbit. Using a form of primer-vector theory the problem is formulated in a way that leads to relatively easy calculation of
the optimal velocity increments. A certain vector that can easily be calculated from the boundary conditions determines the
number of impulses required for solution of the optimization problem and also is useful in the computation of these velocity
increments. Necessary and sufficient conditions for boundary conditions to require exactly three nonsingular non-degenerate
impulses for solution of the related optimal rendezvous problem, and a means of calculating these velocity increments are
presented. A simple example of a three-impulse rendezvous problem is solved and the resulting trajectory is depicted. Optimal
non-degenerate nonsingular two-impulse rendezvous for the related problem is found to consist of four categories of solutions
depending on the four ways the primer vector locus intersects the unit circle. Necessary and sufficient conditions for each
category of solutions are presented. The region of the boundary values that admit each category of solutions of the related
problem are found, and in each case a closed-form solution of the optimal velocity increments is presented. Similar results
are presented for the simpler optimal rendezvous that require only one-impulse. For brevity degenerate and singular solutions
are not discussed in detail, but should be presented in a following study. Although this approach is thought to provide simpler
computations than existing methods, its main contribution may be in establishing a new approach to the more general problem. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
