Polar and axial vectors versus quaternions

American Journal of Physics

Volumn 70, Issue 9, 2002, Pages 958-963

  Silva, Cibelle Celestino ^a   De Martins, Robertode Andra ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748936091     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1475326     Document Type: Article

References (35)

1. E. T. Whittaker A History of Theories of Aether and Alectricily (Humanities Press New York 1973) Vol. 1.
2. James Clerk Maxwell Treatise on Electricity and Magnetism (Dover New York 1954).
3. Reginald J. Stephenson "Development of vector analysis from quaternions, " Am. J. Phys. 34 194-201 (1966).
4. Alfred M. Bork "Vector versus quaternions - The letters in Nature, " Am. J. Phys. 34 202-211 (1966).
5. P. Kelland and P. G. Tait Introduction to Quaternions with Numerous Examples (MacMillan and Co. London 1873); H. T. Flint "Applications of quaternions to the theory of relativity, " Philos. Mag. 39 439-449 (1920); L. Silberstein "Quaternionic form of relativity, " Philos. Mag. 23 790-809 (1912).
6. David Hestenes "Vectors spinors and the complex numbers in classical and quantum physics, " Am. J. Phys. 39 1013-1027 (1971).
7. David Hestenes New Foundations for Classical Mechanics (Kluwer Dordrecht 1999).
8. Jack B. Kuipers Quaternions and Rotation Sequences a Primer with Applications to Orbits Aerospace and Virtual Reality (Princeton U.P. Princeton 1999) p. 105.
9. Reference 8 p. 114.
10. Simon L. Altmann Rotations Quaternions and Double Groups (Clarendon Oxford 1986) p. 9.
11. Reference 10 p. 63.
12. Reference 10 p. 205.
13. William R. Hamilton Elements of Quaternions (Chelsea New York 1969).
14. Michael J. Crowe A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (University of Notre Dame Press London 1967) p. 5.
15. B. L. Van der Waerden "Hamilton's discovery of quaternions, " Math. Mag. 49 (5) 227-234 (1976); John O'Neill "Formalism Hamilton and complex numbers, " Stud. Hist. Philos. Sci. 17 351-372 (1986).
16. Reference 13 Vol. I pp. 135-136 and 158-159. See also Ref. 10 pp. 47-48.
17. Altmann argues that the identification of unit quaternions with rotations by π/2 is unacceptable in the study of the rotation group. See Ref. 10 p. 16.
18. Peter G. Tait An Elementary Treatise on Quaternions (Cambridge U.P. Cambridge 1873) 2nd ed. pp. 34-40.
19. The phrases "polar vector" and "axial vector" were introduced in Wolde-mar Voigt Kompendium der theoretischen Physik (Leipzig 1896) Vol. II p. 418.
20. Reference 13 Vol. I pp. 242 and 335-345; Ref. 18 p. 37.
21. Reference 18 p. 37 (his emphasis).
22. Reference 18 p. 40.
23. James. C. Maxwell Treatise on Electricity and Magnetism (Dover New York 1954) Vol. I p. 9.
24. Lynde P. Wheeler Josiah Willard Gibbs The History of a Great Mind (Ox Bow Woodbridge 1979) pp. 107-109; Paul J. Nahin Oliver Heaviside: Sage in Solitude (IEEE Press New York 1988) p. 22.
25. Josiah W. Gibbs The Scientific Papers of J. Willard Gibbs (Dover New York 1961) p. 20.
26. Reference 25 p. 21.
27. As a matter of fact Heaviside used bold letters to represent vector but we will use italic letters to be consistent with the remainder of the text of our paper.
28. O1iver Heaviside Electromagnetic Theory (Chelsea New York 1971) Vol. I p. 271 (his emphasis).
29. Reference 28 p. 271.
30. Oliver Heaviside Electrical Papers (Chelsea New York 1970) Vol. II p. 3.
31. Reference 28 p. 303.
32. Reference 14 pp. 182-224.
33. Alexander MacFarlane "Vectors and quaternions, " Nature (London) 48 540-541 (1893).
34. Woldemar Voigt Lehrbuch der Kristallphysik (Druck und Verlag Leipzig 1910) p. 130.
35. Paul Langevin "Notions Géométriques Fondamentales, " Encyclópedie des Sciences Mathemaliques Vol. V 1912 p. 3.