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 JAMP  Vol.3 No.5 , May 2015
The Kinetic Energy Formula for the Closed Planar Homothetic Inverse Motions in Complex Plane
Abstract: In this paper, the kinetic energy formula was expressed during one-parameter closed planar homothetic inverse motions in complex plane. Then the relation between the kinetic energy formula and the Steiner formula was given. As an example the sagittal motion of a telescopic crane was considered. This motion was described by a double hinge consisting of the fixed control panel of telescopic crane and the moving arm of telescopic crane. The results were applied to experimentally measured motion.
Cite this paper: Sener, O. and Tutar, A. (2015) The Kinetic Energy Formula for the Closed Planar Homothetic Inverse Motions in Complex Plane. Journal of Applied Mathematics and Physics, 3, 556-562. doi: 10.4236/jamp.2015.35068.
References

[1]   Steiner, J. (1840) Von dem Krummungs-Schwerpuncte Ebener Curven. Journal fur die Reine und Angewandte Mathematik, 21, 33-63.
http://dx.doi.org/10.1515/crll.1840.21.33

[2]   Tutar, A. and Kuruoglu, N. (1996) The Steiner Formula and the Holditch Theorem for the Homothetic Motions on the Planar Kinematics. Mechanism and Machine Theory, 34, 1-6.
http://dx.doi.org/10.1016/S0094-114X(98)00028-7

[3]   Muller, H.R. (1978) Verallgemeinerung einer Formel von Steiner. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, 29, 107-113.

[4]   Muller, H.R. (1978) Uber Tragheitsmomente bei Steinerscher Massenbelegung. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, 29, 115-119.

[5]   Dathe, H. and Gezzi, R. (2014) Addenda and Erratum to: Characteristic Directions of Closed Planar Motions. Zeitschrift fur Angewandte Mathematik und Mechanik, 94, 551-554.
http://dx.doi.org/10.1002/zamm.201300230

[6]   Tutar, A. and Inan, E. (2015) The Formula of Kinetic Energy for the Closed Planar Homothetic Inverse Motions. International Journal of Applied Mathematics, 28.

[7]   Sener, O. and Tutar, A. (2014) The Steiner Formula and the Polar Moment of Inertia for the Closed Planar Homothetic Inverse Motions in Complex Plane. Submitted.

[8]   Dathe, H. and Gezzi, R. (2012) Characteristic Directions of Closed Planar Motions. Zeitschrift fur Angewandte Mathematik und Mechanik, 92, 2-13.
http://dx.doi.org/10.1002/zamm.201100178

 
 
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