More clarity on the concept of material frame-indifference in classical continuum mechanics (Acta Mechanica DOI:10.1007/s00707-008-0028-4);More clarity on the concept of material frame-indifference in classical continuum mechanics

Acta Mechanica

Volumn 202, Issue 1-4, 2009, Pages 213-246

  Frewer, Michael ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MECHANICS; GEOMETRY;

COVARIANT; DIFFERENTIAL GEOMETRY; MATERIAL FRAME INDIFFERENCE; MATHEMATICAL FRAMEWORKS; NEWTONIAN MECHANICS; REYNOLDS-AVERAGED EQUATIONS;

NAVIER STOKES EQUATIONS;

EID: 58149337556     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00707-008-0087-6     Document Type: Erratum

References (74)

1. Haupt P.: Continuum mechanics and theory of materials, 2nd edn. Springer, Heidelberg (2002)
2. Hutter K., Jöhnk K.: Continuum methods of physical modeling. Springer, Heidelberg (2004)
3. Truesdell C., Toupin R.: The classical field theories. In: Flügge, S.(eds) Prinzipien der klassischen Mechanik und Feldtheorie, vol. 2 of Handbuch der Physik, pp. 226-793. Springer, Heidelberg (1960)
4. Truesdell C., Noll W.: The non-linear field theories of mechanics, 3rd edn. Springer, Heidelberg (1965)
5. A.I. Murdoch 2005 On criticism of the nature of objectivity in classical continuum mechanics Continuum. Mech. Thermodyn. 17 135
6. I.-S. Liu 2005 Further remarks on Euclidean objectivity and the principle of material frame-indifference Continuum. Mech. Thermodyn. 17 125
7. Hooke R.: Lectures de potentia restitutiva, or of spring explaining the power of springing bodies, 1678 London. In: Gunther, R.T.(eds) Early science in Oxford, vol VIII, pp. 331-356. Oxford University Press, New York (1931)
8. S.-D. Poisson 1829 Mémoire sur les équations générales de l'équilibre et du mouvement des corps élastiques et des fluides J. École. Poly. 13 1
9. A.-L. Cauchy 1829 Sur l'équilibre et le mouvement intérieur des corps considérés comme des masses continues Ex. de Math. 4 293
10. A. Einstein 1905 Zur Elektrodynamik bewegter Körper Ann. Physik. 17 891
11. Zaremba, S.: Le principe des mouvements relatifs et les équations de la mécanique physique. Bull. Int. Acad. Sci. Cracovie. (1903) 614
12. G. Jaumann 1906 Elektromagnetische Vorgänge in bewegten Medien Sitzungsbericht Akad. Wiss. Wien (IIa) 15 337
13. W. Noll 1964 Euclidean geometry and Minkowskian chronometry Am. Math. Mon. 71 129
14. Noll W.: Space-time structures in classical mechanics. In: Bunge, M.(eds) Delaware seminar in the foundations of physics, pp. 28-34. Springer, Heidelberg (1967)
15. W. Noll 1973 Lectures on the foundations of continuum mechanics and thermodynamics Arch. Rat. Mech. Anal. 52 62
16. I. Müller 1972 On the frame dependence of stress and heat flux Arch. Rational Mech. Anal. 45 241
17. D.G. Edelen J.A. [tmp] McLennan 1973 Material indifference: a principle or a convenience Int. J. Eng. Sci. 11 813
18. C.C. Wang 1975 On the concept of frame-indifference in continuum mechanics and in the kinetic theory of gases Arch. Rat. Mech. Anal. 58 381
19. I. Müller 1976 On the frame dependence of electric current and heat flux in a metal Acta. Mech. 24 117
20. L.H. Söderholm 1976 The principle of material frame-indifference and material equations of gases Int. J. Eng. Sci. 14 523
21. C. Truesdell 1976 Correction of two errors in the kinetic theory of gases which have been used to cast unfounded doubt upon the principle of frame indifference Meccanica 11 196
22. W.G. Hoover B. Moran R.M. More A.J. Ladd 1981 Heat conduction in a rotating disk via nonequilibrium molecular dynamics Phys. Rev. A. 24 2109
23. M. Heckl I. Müller 1983 Frame dependence, entropy, entropy flux, and wave speeds in mixtures of gases Acta. Mech. 50 71
24. A.I. Murdoch 1983 On material frame-indifference, intrinsic spin, and certain constitutive relations motivated by the kinetic theory of gases Arch. Rat. Mech. Anal. 83 185
25. G. Ryskin 1985 Misconception which led to the "material frame-indifference" controversy Phys. Rev. A. 32 1239
26. T. Matolcsi 1986 On material frame-indifference Arch. Rat. Mech. Anal. 91 99
27. L.J. Kempers 1989 The principle of material frame indifference and the covariance principle Il Nuovo. Cimento B. 103 227
28. A. Einstein 1916 Die Grundlage der allgemeinen Relativitätstheorie Ann. Physik. 49 769
29. F.M. Sharipov G.M. Kremer 1995 On the frame dependence of constitutive equations. I. Heat transfer through a rarefied gas between two rotating cylinders Cont. Mech. Thermodyn. 7 57
30. T. Matolcsi T. Gruber 1996 Spacetime without reference frames: an application to the kinetic theory Int. J. Theor. Phys. 35 1523
31. W. Muschik 1998 Objectivity and frame indifference, revisited Arch. Mech. 50 541
32. B. Svendsen A. Bertram 1999 On frame-indifference and form-invariance in constitutive theory Acta Mech. 132 195
33. A. Bertram B. Svendsen 2001 On material objectivity and reduced constitutive equations Arch. Mech. 53 653
34. R.S. Rivlin 2002 Material symmetry revisited GAMM-Mitteilungen 25 1/2 109
35. A. Bertram B. Svendsen 2004 Reply to Rivlin's material symmetry revisited or much ado about nothing GAMM-Mitteilungen 27 1/2 88
36. A.I. Murdoch 2003 Objectivity in classical continuum physics: a rationale for discarding the 'principle of invariance under superposed rigid body motions' in favour of purely objective considerations Continuum. Mech. Thermodyn. 15 309
37. I.-S. Liu 2004 On Euclidean objectivity and the principle of material frame-indifference Continuum. Mech. Thermodyn. 16 177
38. W. Noll 2006 A frame-free formulation of elasticity J. Elast. 83 291
39. J.L. Lumley 1970 Toward a turbulent constitutive relation J. Fluid. Mech. 41 413
40. J.L. Lumley 1983 Turbulence modeling J. Appl. Mech. 50 1097
41. C.G. Speziale 1981 Some interesting properties of two-dimensional turbulence Phys. Fluids. 24 1425
42. C.G. Speziale 1998 A review of material frame-indifference in mechanics Appl. Mech. Rev. 51 489
43. A. Sadiki K. Hutter 1996 On the frame dependence and form invariance of the transport equations for the Reynolds stress tensor and the turbulent heat flux vector: its consequences on closure models in turbulence modelling Cont. Mech. Thermodyn. 8 341
44. Schutz B.: Geometrical methods of mathematical physics. Cambridge University Press, Cambridge (1980)
45. Schrödinger E.: Space-time structure, 4th edn. Cambridge University Press, London (1985)
46. Sexl R.U., Urbantke H.K.: Relativity, groups, particles: special relativity and relativistic symmetry in field and particle physics, 2nd edn. Springer, Heidelberg (2001)
47. Ovsiannikov L.V.: Group analysis of differential equations, 2nd edn. Academic Press, New York (1982)
48. Olver P.J.: Applications of Lie groups to differential equations, 2nd edn. Springer, Heidelberg (1993)
49. Ibragimov N.H.: Lie group analysis of differential equations, vol. I-III of CRC Handbook. CRC Press, Boca Raton (1994)
50. Bluman G.W., Kumei S.: Symmetries and differential equations, 2nd edn. Springer, Heidelberg (1996)
51. Cantwell B.J.: Introduction to symmetry analysis. Cambridge University Press, London (2002)
52. G.B. Hess W.M. Fairbank 1967 Measurements of angular momentum in superfluid helium Phys. Rev. Lett. 19 216
53. L. Landau 1941 Theory of the superfluidity of Helium II Phys. Rev. 60 356
54. Misner C.W., Thorne K.S., Wheeler J.A.: Gravitation. Freeman, San Fransisco (1973)
55. Stephani H.: General relativity: an introduction to the theory of the gravitational field, 2nd edn. Cambridge University Press, London (1990)
56. Fließbach T.: Allgemeine Relativitätstheorie, 5th edn. Spektrum, New York (2006)
57. Friedman M.: Foundations of space-time theories: relativistic physics and philosophy of science. Princeton University Press, New Jersey (1983)
58. Barbour J.B., Pfister H.: Mach's principle: from Newton's bucket to quantum gravity. Birkhäuser, Basel (1995)
59. Barbour J.B.: The discovery of dynamics: a study from a Machian point of view of the discovery and the structure of dynamical theories. Oxford University Press, New York (2001)
60. Penrose, R.: The road to reality: a complete guide to the laws of the universe. Alfred A. Knopf Publishing, (2005)
61. Mach, E.: Die Mechanik in ihrer Entwicklung, Wissenschaftiche Buchgesellschaft Darmstadt, Reprografischer Nachdruck 1991, 9th edn (1883)
62. Barbour J.B.: Absolute or relative motion: the deep structure of general relativity. Oxford University Press, New York (2004)
63. E. Kretschmann 1917 Über den physikalischen Sinn der Relativitätspostulate, A. Einsteins neue und seine ursprüngliche Relativitätstheorie Ann. Physik 53 575
64. A. Einstein 1918 Dialog über Einwände gegen die Relativitätstheorie Naturwissenschaften 6 697
65. A. Einstein 1918 Prinzipielles zur allgemeinen Relativitätstheorie Ann. Physik. 55 241
66. J.D. Norton 1993 General covariance and the foundations of general relativity: eight decades of dispute Rep. Prog. Phys. 56 791
67. J.D. Norton 1995 Did Einstein stumble? The debate over general covariance Erkenntnis, Kluwer 42 223
68. D. Dieks 2006 Another look at general covariance and the equivalence of reference frames Stud. Hist. Philos. Modern. Phys. 37 174
69. T. Matolcsi P. Ván 2007 Absolute time derivatives J. Math. Phys. 48 053507
70. E. Cartan 1923 Sur les variétés à connexion affine et la théorie de la relativité généralisée Annales scientifiques de l'École Normale Supérieure 40 325
71. K. Friedrichs 1928 Eine invariante Formulierung des Newtonschen Gravitationsgesetzes und des Grenzüberganges vom Einsteinschen zum Newtonschen Gesetz Math. Ann. 98 566
72. P. Havas 1964 Four-dimensional formulations of Newtonian mechanics and their relation to the special and the general theory of relativity Rev. Mod. Phys. 36 938
73. Trautman A. (1966) Comparison of Newtonian and relativistic theories of space-time. In: Hoffmann B. (eds). Perspectives in geometry and relativity. Indiana University Press, Bloomington
74. Ehlers, J.: The Newtonian limit of general relativity. In: Ferrarese, G. (ed.) Classical mechanics and relativity: relationship and consistency, Bibliopolis (1991)