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2018 | 97 | 153-167
Article title

Relativistic motion of classical charged particles in a uniform electromagnetic field

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Abstracts
EN
Here we show the importance of a systematic method to generate any integer power of a matrix in 2, 3 and 4 dimensions. This is motivated by the integration of Frenet–Serret formulae for the case of constant curvatures, and by the relativistic motion of a point charge into a homogeneous electromagnetic field, because in such situations it is necessary to calculate being a scalar. By these reasons, we believe that this work can be useful for people interested in linear algebra, differential geometry and electrodynamics.
Discipline
Year
Volume
97
Pages
153-167
Physical description
References
  • [1] J. L. Synge, Proc. Roy. Irish Acad. A65 (1967) 27-42.
  • [2] C. Lanczos, Space through the ages, Academic Press, London (1970).
  • [3] E. Honig, E. L. Schucking, C.V. Vishveshwara, J. Math. Phys. 15(6) (1974) 774-781.
  • [4] D. J. Struik, Lectures on classical differential geometry, Dover, New York (1988).
  • [5] J. López-Bonilla, G. Ovando, J. Rivera, Proc. Indian Acad. Sci. (Math. Sci.) 107(1) (1997) 43-55.
  • [6] J. López-Bonilla, G. Ovando, J. Rivera, J. Moscow Phys. Soc. 9 (1999) 83-88.
  • [7] J. H. Caltenco, R. Linares, J. López-Bonilla, Czech. J. Phys. 52(7) (2002) 839-842.
  • [8] J. H. Caltenco, J. López-Bonilla, R. Peña, Indian J. Theor. Phys. 52(3) 82004) 179-183.
  • [9] J. H. Caltenco, J. López-Bonilla, R. Peña, Bol. Soc. Cub. Mat. Comp. 7(2) (2009) 121-128.
  • [10] J. L. Synge, Proc. Roy. Irish Acad. A66 (1968) 41-68.
  • [11] H. Goldstein, Classical mechanics, Addison-Wesley, Mass. (1980).
  • [12] J. L. Synge, Relativity: the special theory, North-Holland, Amsterdam (1965).
  • [13] J. L. Synge, Ann. Mat. Pura Appl. 84 (1970) 33-60.
  • [14] J. Plebañski, Bull. Acad. Polon. Sci. Cl. 9 (1961) 587-593.
  • [15] E. Piña, Rev. Mex. Fís. 16 (1967) 233-236.
  • [16] H. Wayland, Quart. Appl. Math. 2 (1945) 277-306.
  • [17] H. Takeno, Tensor N.S. 3 (1954) 119-122.
  • [18] C. Lanczos, Applied analysis, Dover, New York (1988).
  • [19] J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford (1965).
  • [20] J. H. Caltenco, J. López-Bonilla, R. Peña-Rivero, Aligarh Bull. Maths. 19 (2000) 55-59.
  • [21] D. Lovelock, H. Rund, Tensors, differential forms, and variational principles, John Wiley and Sons, New York (1975).
  • [22] C. Lanczos, J. Res. Nat. Bur. Stand. 45(4) (1950) 255-282.
  • [23] J. B. Rosser, C. Lanczos, M. R. Hestenes, W. Karush, J. Res. Nat. Bur. Stand. 47(4) (1951) 291-297.
  • [24] H. E. Salzer, J. Res. Nat. Bur. Stand. 49(2) (1952) 133-134.
  • [25] B. K. P. Scaife, Studies in numerical analysis, Academic Press, New York (1974).
  • [26] U. J. Leverrier, J. de Math. 5 (1840) 220-254.
  • [27] A. N. Krylov, Bull. de l’ Acad. Sci. URSS 7(4) (1931) 491-539.
  • [28] P. Horst, Ann. Math. Stat. 6 (1935) 83-84.
  • [29] A. S. Householder, F. L. Bauer, Numerische Math. 1 (1959) 29-37.
  • [30] I. Guerrero M., J. López-Bonilla, J. Rivera R., J. Inst. Eng. (Nepal) 8(1-2) (2011) 255-258.
  • [31] M. P. Drazin, The Math. Gaz. 36 (1952) 253-255.
  • [32] J. López-Bonilla, Rev. Colomb. Fís. 17 (1985) 1-20.
  • [33] F. B. Hildebrand, Methods of applied mathematics, Prentice-Hall, New York (1965).
  • [34] A. Taub, Phys. Rev. 73(2) (1948) 786-798.
  • [35] G. Muñoz, Am. J. Phys. 65(5) (1997) 429-433.
  • [36] Y. Friedman, M. M. Danziger, PIERS 4(5) (2008) 531-535.
  • [37] G. F. Torres del Castillo, C. Sosa-Sánchez, Rev. Mex. Fís. 57(1) (2011) 53-59.
  • [38] G. Arreaga, J. Saucedo, Palestine J. Maths. 3(2) (2014) 218-230.
  • [39] G. Altay Suroglu, Open Phys. 16 (2018) 14-20.
Document Type
article
Publication order reference
YADDA identifier
bwmeta1.element.psjd-0f0d1e9f-68bd-4215-82a9-0bd087b2d46b
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