Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions of the Wheeler-Feynman equations with discontinuous velocities   We generalize Wheeler-Feynman electrodynamics with a variational
boundary-value problem with past and future boundary segments that can include
velocity discontinuity points. Critical-point trajectories must satisfy the
Euler-Lagrange equations of the action functional, which are
neutral-differential delay equations of motion (the Wheeler-Feynman equations
of motion). At velocity discontinuity points, critical-point orbits must
satisfy the Weierstrass-Erdmann conditions of continuity of partial momenta and
partial energies. We study a special class of boundary data having the shortest
time-separation between boundary segments, for which case the Wheeler-Feynman
equations reduce to a two-point boundary problem for an ordinary differential
equation. For this simple case we prove that the extended variational problem
has solutions with discontinuous velocities. We construct a numerical method to
solve the Wheeler-Feynman equations together with the Weierstrass-Erdmann
conditions and calculate some numerical orbits with discontinuous velocities.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph