Noether's theorem in a rotating reference frame

American Journal of Physics

Volumn 79, Issue 3, 2011, Pages 326-332

  Dallen, Lucas ^a   Neuenschwander, Dwight E ^a  

^a Southern Nazarene University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79951618994     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.3535582     Document Type: Article

References (38)

1. Noether E. Invariante variationsprobleme. Nachr. Akad. Will. Göttingen, Math.-Phys. Kl. II 1918, 1918:235-257. , .
2. Noether E. Tavel M. Invariant variation problems. Transp. Theory Stat. Phys. 1971, 1:186-207. TTSPB4, 0041-1450, 10.1080/00411457108231446
3. Neuenschwander D. Emmy Noether's Wonderful Theorem 2011, (Johns Hopkins U. P., Baltimore, MD, ).
4. Logan J. Invariant Variational Principles 1977, (Academic, New York, ).
5. The Association of Women in Mathematics sponsors the annual Noether Lectures 〈〉 to honor women who have made fundamental and sustained contributions to the mathematical sciences.
6. Abers E.S. Lee B.W. Gauge theories. Phys. Rep. 1973, 9:1-2. PRPLCM, 0370-1573, 10.1016/0370-1573(73)90027-6
7. Marion J. Thornton S. Classical Dynamics of Particles and Systems 2004 5th ed. (Brooks/Cole, Belmont, CA, ).
8. Taylor J. Classical Mechanics 2005, (University Science Books, Sausalito, CA, ).
9. Finkelstein R. Nonrelativistic Mechanics 1973, (W. A. Benjamin, Reading, MA, ).
10. Goldstein H. Classical Mechanics 1965, (Addison-Wesley, Reading, MA, ).
11. Symon K. Mechanics 1953, (Addison-Wesley, Cambridge, MA, ).
12. Campbell J.W. An Introduction to Mechanics 1947, (Pitman, New York, ).
13. Neuenschwander D. Starkey S. Adiabatic invariance derived from the Rund-Trautman identity and Noether's theorem. Am. J. Phys. 1993, 61(11):1008-1013. AJPIAS, 0002-9505, 10.1119/1.17383, and, .
14. Neuenschwander D. Taylor G. The adiabatic invariants of plasma physics derived from the Rund-Trautman identity and Noether's theorem. Am. J. Phys. 1996, 64(11):1428-1430. AJPIAS, 0002-9505, 10.1119/1.18396, and, .
15. Ferrario C. Neuenschwander D. Taylor G. Comments on 'The adiabatic invariants of plasma physics derived from the Rund-Trautman identity and Noether's theorem'. Am. J. Phys. 1998, 66(11):1016-1017. AJPIAS, 0002-9505, 10.1119/1.19013, and, .
16. Giordano C.M. Plastino A.R. Noether's theorem, rotating potentials, and Jacobi's integral of motion. Am. J. Phys. 1998, 66(11):989-995. AJPIAS, 0002-9505, 10.1119/1.19011, and, .
17. Turner B. A Hamiltonian for geometrical optics. J. Undergrad. Res. Phys. 1991, 10(1):23-28. , .
18. Srednicki M. Quantum Field Theory 2007, (Cambridge U. P., New York, ), Chap. 22.
19. Pais A. The Science and Life of Albert Einstein 1982, 276. (Oxford U. P., New York, ), p.
20. Georgi H. Macmillan Encyclopedia of Physics 1996, 1:249-252. (Simon and Schuster Macmillan, New York, ), Vol., pp.
21. Peacock J. Cosmological Physics 1999, 217-218. (Cambridge U. P., New York, ), pp.
22. Ramond P. Field Theory: A Modern Primer 1981, 38. (Benjamin/Cummings, Reading, MA, ), p.
23. Hand L. Finch J. Analytical Mechanics 1998, and, (Cambridge U. P., Cambridge, ).
24. Padmanabhan T. Theoretical Astrophysics: Vol. 1, Astrophysical Processes 2000, (Cambridge U. P., Cambridge, ).
25. Neuenschwander D. When 'F' does not equal 'ma'. SPS Observer 2001, 33:10-14. ,, .
26. rI)=U(r+S)=U(r)+S{dot operator}∇U(r)+....
27. Lopez L.F. Coutinho F.A. B. Motion of articulated bodies: An application of gauge invariance in classical Lagrangian mechanics. Am. J. Phys. 1997, 65(6):528-536. AJPIAS, 0002-9505, 10.1119/1.18584, and, .
28. Trautman A. Noether's equations and conservation laws. Commun. Math. Phys. 1967, 6:248-261. CMPHAY, 0010-3616, 10.1007/BF01646018
29. Rund H. A direct approach to Noether's theorem in the calculus of variations. Util. Math. 1972, 2:205-214. ZZZZZZ, 0315-3681
30. t'/dt is replaced by the Jacobian, and L by the Lagrangian density.
31. (∂ζ/∂t)I=0, so that in the Park frame, ζ=const. If ζ is not proportional to ω, then its being constant in the Park frame would mean it rotates as observed in the Carousel frame and not be constant. Thus, if ζ is to be constant in both frames, it must be parallel or antiparallel to ω.
32. Aitchison I.J. R. Hey A.J. G. Gauge Theories in Particle Physics 1982, 52. and, (Adam Hilger, Bristol, ), p.
33. Bjorken J. Drell S. Relativistic Quantum Mechanics 1964, 10. and, (McGraw-Hill, New York, ), p. ; see also p.
34. Hestenes D. Modeling games in the Newtonian world. Am. J. Phys. 1992, 60(8):732-748. AJPIAS, 0002-9505, 10.1119/1.17080, .
35. Poincaré H. Science and Method 1908, (Barnes and Noble, New York, ) (Barnes and Noble, New York, ) (reprint).
36. Bronowski J. Science and Human Values 1956, (Harper Torchbooks, New York, ).
37. Pirsig R. Zen and the Art of Motorcycle Maintenance 1974, (Morrow, New York, ).
38. Rothman T. Sudarshan G. Doubt and Certainty 1998, and, (Basic Books, New York, ).