Can Mechanically Extended Sources of Radiation in Classical Electrodynamics Solve all Problems of Radiating Point-Like Sources?

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On simple example is shown that a model of mechanically extended source of radiation in classical electrodynamics indeed has some problems with radiation reaction force. So one cannot, in general case, state, that the present situation with classical dynamics of mechanically extended sources of radiation is "very satisfactory".
6 pages, LATEX; v2: more simple method (compared with the previous version) to derive main conclusions of the paper is used. v3: a few modifications are added do not changing the main conclusion of the paper

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