TABLE OF CONTENTS The solution of the flight vehicle s equations of motion describing the accelerations of the center of mass of the vehicle, using stepwise numerical integration methods, is known as Cowell s method59. This method of propagation is generally used in three-DOF simulations where the rotational motion is not considered and does not effect the motion of the center of mass of the space vehicle. When using Cowell s method to propagate space vehicle motion, all of the perturbing accelerations can be included, and a very accurate simulation of the motion results. We can include, for instance, the perturbing effects of the nonspherical gravitational fields given by Eqs. (4.20), the effects of the atmospheric forces that may be acting on the vehicle as given by Eq. (4.106), and all other forces that we are able to describe in the differential equations of motion. Because many astrodynamic equations of motion have no closed-integral solutions, Cowell s method must be applied. Modern digital computer systems are now available and are designed for these types of problems. These computer systems make it possible to solve even the most complicated differential equations of motion using Cowell s method.
The integral lists given in Appendix C.1 can be used to describe the state vectors for each center of mass in the numerical solution of the differential equations of motion. These differential equations of motion should be written to be continuous over the step-size intervals. For instance, the simulation step size should be...
