The application of the solid-angle theorem in the special theory of relativity |
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| Institution: | 1. Indian Statistical Institute, 203 B.T. Road, Kolkata-700108, India;2. Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam, India;3. Narasinha Dutt College, 129, Belilious Road, Howrah-711101, India;1. Université d''Orléans, Observatoire des Sciences de l''Univers en région Centre (OSUC), UMS 3116, 1A rue de la Férollerie, 45071 Orléans, France;2. Université d''Orléans, Collegium Sciences et Techniques (COST), Pôle de Physique, Rue de Chartres, 45100 Orléans, France;3. Centre Nationale de la Recherche Scientifique (CNRS), Laboratoire de Physique et Chimie de l''Environnement et de l''Espace (LPC2E), UMR 7328, Campus CNRS, 3A Av. de la Recherche Scientifique, 45071 Orléans, France;4. Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Xavier Sigaud 150, 22290-180 Urca, Rio de Janeiro, RJ, Brasil |
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| Abstract: | Ishlinskii's theorem, well known in classical mechanics, asserts that if an axis, selected in a rigid body, having zero projection of the angular velocity onto this axis, described a closed conical surface during the motion of the body, then, after the axis has returned to its initial position the body will have described an angle around it numerically equal to solid angle of the described cone. It is shown that the same relation also exists in the Special Theory of Relativity—the angle of rotation described by a rigid body during motion along a curvilinear trajectory due to the Thomas precession effect, is numerically equal to the solid angle observed in a fixed frame of reference described by an axis connected with the body due to a change in the rotation of the image of the rigid body. The latter phenomenon is due to the Lorentz contraction of the length and the retardation of light radiated by different parts of the body 10–13]. |
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