ISBN-10: 0120121034

ISBN-13: 9780120121038

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B) Change the step size based on an error criterion. (c) Restart the integration when discontinuities are introduced. While some of these functions can be performed by the user, it is more convenient and faster t o have these built into the integration subroutine. The flexibility features affect both the speed of the integration and the accuracy of the results. Frequent interruption of the basic integrating routine results in increased computing time because the restarting procedure, except for Runge-Kutta methods, is expensive and also tends to reduce accuracy although the exact reason for this is not clear.

It is clear that these equations are considerably more complicated to program than the Cowell equations and that the computing time per step is considerably greater. Moreover, the two body formulas must still be solved a t every step since the perturbations are expressed in rectangular coordinates. In addition, accuracy is difficult to maintain on low eccentricity orbit as can be seen from the computation of v' and subsequently of M'. For low eccentricity orbits a different set of parameters which avoids the small divisor problem has been proposed by Herrick and is described in his book [62].

A Runge-Kutta method of this type is the following : kl = hf(xn, 2 / n ) , yn+1 = yn + h [ Y f . 9) SATELLITE ORBIT TRAJECTORIES 25 This method has a local truncation error of order h5 just as the corresponding method for first order equations, but involves only three derivative evaluations instead of four. A saving of about 25% in computation time for the same accuracy thus appears possible. 10) The apparent advantage of this method is that a local truncation error of order h6 is achieved compared to an h5 error for similar formulas for firstorder systems.

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Advances in Computers, Vol. 3

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