Skip to main content
Erschienen in: Measurement Techniques 1/2013

01.04.2013 | General Problems of Metrology and Measurement Technique

On the Dimensionality of Dimensionless Quantities

verfasst von: A. N. Mitrokhin

Erschienen in: Measurement Techniques | Ausgabe 1/2013

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The possibility of establishing a relationship among the conceptual apparatus of mathematics, physics, and metrology with a change in the requirement for the formation of the SI units of measurement is examined on the basis of new approaches to mathematical operations, including the introduction of the new concept of a qualitative (dimensional) unit.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat P. C. Bridgeman, Dimensional Analysis [Russian translation by S. I. Vavilov], Gostekhteoretizdat, Moscow (1934). P. C. Bridgeman, Dimensional Analysis [Russian translation by S. I. Vavilov], Gostekhteoretizdat, Moscow (1934).
2.
Zurück zum Zitat V. A. Venikov, Applications of the Theory of Similarity and Physical Modelling in Electrical Technology [in Russian], Gosenergoizdat, Moscow, Leningrad (1949). V. A. Venikov, Applications of the Theory of Similarity and Physical Modelling in Electrical Technology [in Russian], Gosenergoizdat, Moscow, Leningrad (1949).
3.
Zurück zum Zitat L. I. Sedov, Similarity and Dimensional Methods in Mechanics [in Russian], Nauka, Moscow (1977). L. I. Sedov, Similarity and Dimensional Methods in Mechanics [in Russian], Nauka, Moscow (1977).
4.
Zurück zum Zitat D. C. Dixon, “Another viewpoint on plane angle,” Metrologia, 22, 245–250 (1986).ADSCrossRef D. C. Dixon, “Another viewpoint on plane angle,” Metrologia, 22, 245–250 (1986).ADSCrossRef
5.
Zurück zum Zitat Yu. V. Tarbeeva (ed.), Basic Terminology in the Area of Metrology: A Dictionary-Handbook [in Russian], Izd. Standartov, Moscow (1989). Yu. V. Tarbeeva (ed.), Basic Terminology in the Area of Metrology: A Dictionary-Handbook [in Russian], Izd. Standartov, Moscow (1989).
6.
7.
Zurück zum Zitat V. I. Daineko et al., A Memorandum for Solution of Computational Problems in Chemistry (for students and teachers), Intellekt, Moscow (1997). V. I. Daineko et al., A Memorandum for Solution of Computational Problems in Chemistry (for students and teachers), Intellekt, Moscow (1997).
8.
Zurück zum Zitat I. Sh. Kogan, “On dimensionality and units of measurement for dimensionless physical quantities,” Zakonodat. Prikl. Metrol., No. 4, 55–57 (1998). I. Sh. Kogan, “On dimensionality and units of measurement for dimensionless physical quantities,” Zakonodat. Prikl. Metrol., No. 4, 55–57 (1998).
9.
Zurück zum Zitat RMG 29-99, Metrology. Basic Terminology and Definitions. RMG 29-99, Metrology. Basic Terminology and Definitions.
10.
Zurück zum Zitat I. M. Mills, B. N. Taylor, and A. J. Thor, “Definitions of the units radian, neper, bel, and decibel,” Metrologia, 38, 353–361 (2001).ADSCrossRef I. M. Mills, B. N. Taylor, and A. J. Thor, “Definitions of the units radian, neper, bel, and decibel,” Metrologia, 38, 353–361 (2001).ADSCrossRef
11.
Zurück zum Zitat GOST 8.417-2002, State System for Support of the Uniformity of Measurements. Units of Quantities. GOST 8.417-2002, State System for Support of the Uniformity of Measurements. Units of Quantities.
12.
Zurück zum Zitat ISO 80000-3:2006 (R), Quantities and Units. Part 3. Space and Time. ISO 80000-3:2006 (R), Quantities and Units. Part 3. Space and Time.
13.
Zurück zum Zitat ISO 80000-1:2009 (E), Quantities and Units. Part 1. General Assumptions. ISO 80000-1:2009 (E), Quantities and Units. Part 1. General Assumptions.
14.
Zurück zum Zitat International Dictionary of Metrology: Basic and General Concepts and Corresponding Terminology [Russian translation from English and French], 2nd revised ed., VNIIM im. D. I. Mendeleeva, NPO Professional, St. Petersburg (2010). International Dictionary of Metrology: Basic and General Concepts and Corresponding Terminology [Russian translation from English and French], 2nd revised ed., VNIIM im. D. I. Mendeleeva, NPO Professional, St. Petersburg (2010).
15.
Zurück zum Zitat A. N. Mitrokhin, On the Interaction of Dimensionalities in Mathematical Transformations [in Russian], Transport, Moscow (1996). A. N. Mitrokhin, On the Interaction of Dimensionalities in Mathematical Transformations [in Russian], Transport, Moscow (1996).
16.
Zurück zum Zitat I. Sh. Kogan, “A physical quantity should not have units of m−1 or sec−1,” Zakonodat. Prikl. Metrol., No. 5, 43–49 (2011). I. Sh. Kogan, “A physical quantity should not have units of m−1 or sec−1,” Zakonodat. Prikl. Metrol., No. 5, 43–49 (2011).
Metadaten
Titel
On the Dimensionality of Dimensionless Quantities
verfasst von
A. N. Mitrokhin
Publikationsdatum
01.04.2013
Verlag
Springer US
Erschienen in
Measurement Techniques / Ausgabe 1/2013
Print ISSN: 0543-1972
Elektronische ISSN: 1573-8906
DOI
https://doi.org/10.1007/s11018-013-0152-y

Weitere Artikel der Ausgabe 1/2013

Measurement Techniques 1/2013 Zur Ausgabe