International Journal of Theoretical Physics

, Volume 15, Issue 9, pp 657–672 | Cite as

On time-dependent transformation in Newtonian mechanics: Formal theory on the relativity of force

  • Shigeru Ohkuro
Article

Abstract

F. Klein's viewpoint of geometry is applied to the discussion of the time-dependent transformation (TDT) in Newtonian mechanics. Formally the vectorial character of transformation and the invariance of the form of Newtonian equations of motion under TDT are assumed. Then it is shown that our conception of force in Newtonian equations satisfies a certain transformation property under TDT, which is different from the case of Galileo and Newton in which force is regarded as an absolute quantity. Our theory also enables one to derive the fictitious forces such as the centrifugal force and Coriolis force. The balance equation between these fictitious forces and those with reversed sign is considered. The centripetal force of the new type and the force depending on angular acceleration are also given.

Keywords

Field Theory Elementary Particle Quantum Field Theory Balance Equation Reversed Sign 

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References

  1. Goldstein, H. (1950).Classical Mechanics (Addison-Wesley, Reading Massachusetts).Google Scholar
  2. Møller, C. (1952).The Theory of Relativity (Oxford University Press, London).Google Scholar
  3. Shimizu, T. (1965).Theory of Nonlinear Oscillations (in Japanese) (Baifūkan, Tokyo).Google Scholar
  4. Yano, K. (1968).Geometry of Connections (in Japanese) (Morikita, Tokyo).Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • Shigeru Ohkuro
    • 1
  1. 1.Department of Applied Physics, Faculty of EngineeringTohoku UniversitySendaiJapan

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