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THE MINKOWSKIAN PLANAR 4R MECHANISM

Year 2012, Volume: 5 Issue: 1, 1 - 35, 30.04.2012

Gábor Hegedüs Brian Moore

Abstract


Keywords

Mechanism Minkowskian space double numbers

References

  • [1] Birman, G. S. and Nomizu, K., Trigonometry in Lorentzian geometry. Amer. Math. Monthly 91 (1984), no. 9, 543–549.
  • [2] Catoni, F., Cannata R., Catoni, V. and Zampetti, P., Hyperbolic trigonometry in two- dimensional space-time geometry. Nuovo Cimento Soc. Ital. Fis. B 118 (2003), no. 5, 475– 492.
  • [3] Catoni, F., Cannata R., Catoni, V. and Zampetti, P., Two-dimensional hypercomplex num- bers and related trigonometries and geometries Adv. Appl. Clifford Algebr. 14 (2004), no. 1, 47–68.
  • [4] Ergin, A. A., On the 1-parameter Lorentzian motions, Comm. Fac. Sci. Univ. Ankara Ser. A1 Math. Statist. 40 (1991), 59–66.
  • [5] Einstein, A., Zur Elektrodynamik bewegter K¨orper, Annalen der Physik 322, (1905) Issue 10, 895–921.
  • [6] Fjelstad, P. and Gal, S. G., Two-dimensional geometries, topologies, trigonometries and physics generated by complex-type numbers. Adv. Appl. Clifford Algebras 11 (2001), no. 1, 81–107
  • [7] Gündoğan, H. and Kçilioğlu, O., Lorentzian matrix multiplication and the motions on Lorentzian plane. Glas. Mat. Ser. III 41(61) (2006), no. 2, 329–334.
  • [8] Harkin, A. A. and Harkin, J. B., Geometry of Generalized Complex Numbers. Math. Mag. 77 (2004), no. 2, 118–129.
  • [9] Lie, S. and Scheffers, M. G., Vorlesungen u¨ber continuierliche Gruppen, Kap. 21, Teubner, Leipzig, 1893
  • [10] McCarthy, J. M., Geometric design of linkages. Interdisciplinary Applied Mathematics, 11 Springer-Verlag, New York, 2000.
  • [11] McCarthy, J. M., An Introduction to Theoretical Kinematics, MIT Press, Cambridge, 1990. [12] Myrvold, W.C. and Christian, J., Quantum Reality, Relativistic Causality and closing the epistemic circle, Springer Science+Business Media, 2009.
  • [13] O’Neill, B., Semi-Riemannian Geometry. With Applications to Relativity, Academic Press, Inc., New York, 1983.
  • [14] Nesŏvić, E. and Petrović-Torgašev, M., Some trigonometric relations in the Lorentzian plane. Kragujevac J. Math. 25 (2003), 219–225.
  • [15] Ratcliffe, J. G., Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, 1994.
  • [16] Yaglom, I. M., A simple non-Euclidean geometry and its physical basis. An elementary ac- count of Galilean geometry and the Galilean principle of relativity. Springer-Verlag, New York-Heidelberg, 1979
  • [17] Yüce, S. and Kuruğlu, N., One-parameter plane hyperbolic motions. Adv. Appl. Clifford Algebr. 18 (2008), no. 2, 279–285.

Year 2012, Volume: 5 Issue: 1, 1 - 35, 30.04.2012

Gábor Hegedüs Brian Moore

Abstract

References

  • [1] Birman, G. S. and Nomizu, K., Trigonometry in Lorentzian geometry. Amer. Math. Monthly 91 (1984), no. 9, 543–549.
  • [2] Catoni, F., Cannata R., Catoni, V. and Zampetti, P., Hyperbolic trigonometry in two- dimensional space-time geometry. Nuovo Cimento Soc. Ital. Fis. B 118 (2003), no. 5, 475– 492.
  • [3] Catoni, F., Cannata R., Catoni, V. and Zampetti, P., Two-dimensional hypercomplex num- bers and related trigonometries and geometries Adv. Appl. Clifford Algebr. 14 (2004), no. 1, 47–68.
  • [4] Ergin, A. A., On the 1-parameter Lorentzian motions, Comm. Fac. Sci. Univ. Ankara Ser. A1 Math. Statist. 40 (1991), 59–66.
  • [5] Einstein, A., Zur Elektrodynamik bewegter K¨orper, Annalen der Physik 322, (1905) Issue 10, 895–921.
  • [6] Fjelstad, P. and Gal, S. G., Two-dimensional geometries, topologies, trigonometries and physics generated by complex-type numbers. Adv. Appl. Clifford Algebras 11 (2001), no. 1, 81–107
  • [7] Gündoğan, H. and Kçilioğlu, O., Lorentzian matrix multiplication and the motions on Lorentzian plane. Glas. Mat. Ser. III 41(61) (2006), no. 2, 329–334.
  • [8] Harkin, A. A. and Harkin, J. B., Geometry of Generalized Complex Numbers. Math. Mag. 77 (2004), no. 2, 118–129.
  • [9] Lie, S. and Scheffers, M. G., Vorlesungen u¨ber continuierliche Gruppen, Kap. 21, Teubner, Leipzig, 1893
  • [10] McCarthy, J. M., Geometric design of linkages. Interdisciplinary Applied Mathematics, 11 Springer-Verlag, New York, 2000.
  • [11] McCarthy, J. M., An Introduction to Theoretical Kinematics, MIT Press, Cambridge, 1990. [12] Myrvold, W.C. and Christian, J., Quantum Reality, Relativistic Causality and closing the epistemic circle, Springer Science+Business Media, 2009.
  • [13] O’Neill, B., Semi-Riemannian Geometry. With Applications to Relativity, Academic Press, Inc., New York, 1983.
  • [14] Nesŏvić, E. and Petrović-Torgašev, M., Some trigonometric relations in the Lorentzian plane. Kragujevac J. Math. 25 (2003), 219–225.
  • [15] Ratcliffe, J. G., Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, 1994.
  • [16] Yaglom, I. M., A simple non-Euclidean geometry and its physical basis. An elementary ac- count of Galilean geometry and the Galilean principle of relativity. Springer-Verlag, New York-Heidelberg, 1979
  • [17] Yüce, S. and Kuruğlu, N., One-parameter plane hyperbolic motions. Adv. Appl. Clifford Algebr. 18 (2008), no. 2, 279–285.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Gábor Hegedüs This is me

Brian Moore This is me

Publication Date April 30, 2012
Published in Issue Year 2012 Volume: 5 Issue: 1

Cite

APA Hegedüs, G., & Moore, B. (2012). THE MINKOWSKIAN PLANAR 4R MECHANISM. International Electronic Journal of Geometry, 5(1), 1-35.
AMA Hegedüs G, Moore B. THE MINKOWSKIAN PLANAR 4R MECHANISM. Int. Electron. J. Geom. April 2012;5(1):1-35.
Chicago Hegedüs, Gábor, and Brian Moore. “THE MINKOWSKIAN PLANAR 4R MECHANISM”. International Electronic Journal of Geometry 5, no. 1 (April 2012): 1-35.
EndNote Hegedüs G, Moore B (April 1, 2012) THE MINKOWSKIAN PLANAR 4R MECHANISM. International Electronic Journal of Geometry 5 1 1–35.
IEEE G. Hegedüs and B. Moore, “THE MINKOWSKIAN PLANAR 4R MECHANISM”, Int. Electron. J. Geom., vol. 5, no. 1, pp. 1–35, 2012.
ISNAD Hegedüs, Gábor - Moore, Brian. “THE MINKOWSKIAN PLANAR 4R MECHANISM”. International Electronic Journal of Geometry 5/1 (April 2012), 1-35.
JAMA Hegedüs G, Moore B. THE MINKOWSKIAN PLANAR 4R MECHANISM. Int. Electron. J. Geom. 2012;5:1–35.
MLA Hegedüs, Gábor and Brian Moore. “THE MINKOWSKIAN PLANAR 4R MECHANISM”. International Electronic Journal of Geometry, vol. 5, no. 1, 2012, pp. 1-35.
Vancouver Hegedüs G, Moore B. THE MINKOWSKIAN PLANAR 4R MECHANISM. Int. Electron. J. Geom. 2012;5(1):1-35.