| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Inst Fis, Dept Fis Matemat, BR-05508090 Sao Paulo - Brazil
[2] Univ Fed Sao Carlos, Dept Fis, BR-13565905 Sao Paulo - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Chaos; v. 25, n. 1 JAN 2015. |
| Web of Science Citations: | 1 |
| Abstract | |
We generalize Wheeler-Feynman electrodynamics with a variational boundary value problem for continuous boundary segments that might include velocity discontinuity points. Critical-point orbits must satisfy the Euler-Lagrange equations of the action functional at most points, which are neutral differential delay equations (the Wheeler-Feynman equations of motion). At velocity discontinuity points, critical-point orbits must satisfy the Weierstrass-Erdmann continuity conditions for the partial momenta and the partial energies. We study a special setup having the shortest time-separation between the (infinite-dimensional) boundary segments, for which case the critical-point orbit can be found using a two-point boundary problem for an ordinary differential equation. For this simplest setup, we prove that orbits can have 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. We also prove that the variational boundary value problem has a unique solution depending continuously on boundary data, if the continuous boundary segments have velocity discontinuities along a reduced local space. (C) 2015 Author(s). (AU) | |
| FAPESP's process: | 11/18343-6 - Variational electrodynamics |
| Grantee: | Jayme Vicente de Luca Filho |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 10/16964-0 - Variational Electrodynamics and Electromagnetic Problem of Two and Three Bodies |
| Grantee: | Daniel Câmara de Souza |
| Support Opportunities: | Scholarships in Brazil - Doctorate |