‘Monte carlo’ computer simulation of chain molecules: II. The limiting distribution of end‐to‐end distance for two‐dimensional excluded‐volume chains
A computer technique for simulating configurational behaviour of chains, developed previously, was used to study the nature of the distribution of the magnitude of end-to-end vectors of excluded-volume chains constrained to two dimensions. The study revealed that the above distribution in the limit of infinite chain length deviates greatly from Gaussian behaviour and that the deviation is much greater than for three-dimensional chains. The probability distribution function A exp (—αR5.8) was derived.
The long-term effects of a distant third-body on a massless satellite that is orbiting an oblate body are studied for a high order expansion of the third-body disturbing function. This high order may be required, for instance, for Earth artificial satellites in the so-called MEO region. After filtering analytically the short-period angles via averaging, the evolution of the orbital elements is efficiently integrated numerically with very long step-sizes. The necessity of retaining higher orders in the expansion of the third-body disturbing function becomes apparent when recovering the short-periodic effects required in the computation of reliable osculating elements.