The Two-Body Problem of Classical Electrodynamics
Final rept. 1 Jun 1978-31 May 1979
RHODE ISLAND UNIV KINGSTON DEPT OF MATHEMATICS
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Various competing mathematical models are used in classical electrodynamics. To test, and possibly eliminate, some of these models one can apply them to the two body problem and see whether reasonable results are obtained. In one model it is assumed that each particle is influenced by both the past and future behavior of the other. The special case of two electrons moving symmetrically in one dimension was considered and it was found that this curious model does make sense mathematically provided the two electrons never get too close together. Further studies under this grant led to a simple method for analyzing the asymptotic behavior of solutions problem of certain linear delay differential equations. This is useful in a one-body problem of electrodynamics with radiation reaction,in problems of control theory with time lags, in the telegraph equation, and other applications. Currently work in progress is aimed at understanding the simplest n-body problem of electrodynamics with interactions occurring only through retarded fields.
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