On the torque as a measure of mechanical interaction in the principles of dynamics

• Autorzy: Cveticanin L.

Warianty tytułu

PL

O momencie, jako mierze mechanicznego oddziaływania w zasadach dynamiki

• Języki publikacji: EN

Abstrakty

EN

In most discussions, the Principles of Dynamics are expressed using the force as a measure of mechanical interaction between the bodies. The intention of the paper is to extend the usual discussion on basic theorems, laws and principles in Dynamics of rigid bodies including the torque as another independent measure of mechanical interaction between the bodies. In D’Alambert’s principle of Dynamics, beside the forces, the active and reaction torques are also included. The torque is introduced in the Euler-Newton equations for general motion of the rigid body. The General Equation of Dynamics is reformulated by including the virtual work of the torques on the virtual rotation. An additional view to Newton’s Laws is also given.

PL

W większości rozważań, zasady dynamiki są wyrażane poprzez siły rozumiane jako miary mechanicznych oddziaływań pomiędzy ciałami. Celem tej pracy jest rozszerzenie zwyczajowego podejścia do aksjomatów, praw i zasad dynamiki o pojęcie momentu jako niezależnej miary mechanicznego oddziaływania. Wielkość tę wstawiono do zasady d’Alemberta w postaci momentu czynnego i biernego reakcyjnego. Przedstawiono również momentowe równania Eulera-Newtona dla ogólnego przypadku ruchu bryły sztywnej. Na nowo sformułowano ogólne równanie dynamiki poprzez wstawienie pracy przygotowanej momentu na przemieszczeniu kątowym. Dodatkową dyskusją objęto trzy zasady dynamiki Newtona.

Słowa kluczowe

EN

Newton’s Laws; active and reaction torques; d’Alembert’s principle of dynamics

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2013
• Tom: Vol. 51 nr 1
• Strony: 171--181
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Cveticanin L.

• University of Novi Sad, Faculty of Technical Sciences, Novi Sad, Serbia

Bibliografia

• 1. Birtae P., Casu I., Comanescu D., 2011, Hamilton-Poisson formulation for the rotational motion of a rigid body in the presence of an axisymmetric force field and a gyroscopic torque, Physics Letters A, 375, 3941-3945
• 2. Bohren C.F., 2011, Radiation forces and torques without stress (tensors), Europ. J. Physics, 32, 1515-1518
• 3. Chasles M., 1830, Notes on the general properties of a system of 2 identical bodies randomly located in space; and on the finite or infinitesimal motion of a free solid body, Bull. des Sci. Math., Astron., Phys. et Chim., 14, 321-326 [in French]
• 4. Darwin G.H., 1879, On the precession of a viscous spheroid and on the remote history of the Earth, Philos. Trans. R. Soc., 170, 447-530, http://www.jstor.org/view/02610523/ap000081/00a00010
• 5. Darwin G.H., 1880, On the secular change in the elements of the orbit of a satellite revolving about a tidally distorted planet, Philos. Trans. R. Soc., 171, 713-891
• 6. Djukic D., Jones S.E., 1997, A note on the axioms of Statics, Int. J. Mech. Eng. Edu., 25, 327-330
• 7. Dresselhaus G., 1955, Spin-orbit coupling effects in zinc lende structures, Phys. Rev., 100, 580-586, doi:10.1103/Phys.Rev.100.580
• 8. Efroimsky M., Williams J.G., 2009, Tidal torques: a critical review of some techniques, Celest. Mech. Dyn. Astr., 104, 257-289
• 9. Fujiya H., Kousa P., Fleming B.C., Churcukk D.L., Beynnon B.D., 2011, Effect of muscle loads and torque applied to the tiiba on the strain behavior of the anterior cruciate ligament: An in vitro investigation, Clin. Biomech., 26, 1005-1011
• 10. Gambardella P., Miron I.M., 2011, Current-induced spin-orbit torques, Philos. Trans. R. Soc. A, 369, 3175-3197, http://www.jstor.org/view/02610523/ap000082/00a00200
• 11. Ginsburg J., 2008, Engineering Dynamics, New York, Cambridge University Press
• 12. Hellmann H., 1937, Einfuhrung in die Quantenchemie, Leipzig: Deuticke
• 13. Jiang N.-Q., Fan H.-Y., Wang S., Chen J.-H., Tang L.-Y., Gu W.-J., Cai G.-C., 2011, Virial theorem for angular displacement and torque, Int. J. Theor. Phys., 50, 3610-3615
• 14. Johns O.D., 2005, Analytical Mechanics for Relativity and Quantum Mechanics, New York, Oxford Univeristy Press
• 15. Junge W., Sielaff H., Engelbrecht S., 2009, Torque generation and elastic power transmission in the rotray F0F1-ATPhase, Nature, 459, 364-370, doi:10.1038/nature08145
• 16. Karato S.-I., 2007, Deformation of Earth Materials: An Introduction to the Rheology of Solid Earth, Cambridge, Cambridge University Press, UK
• 17. Liang Q., Zhang D., Wang Y., Ge Y., 2012, Development of a touch probe based on fivedimensional/torque transducer for coordinate measuring machine (CMM), Rob. Comp.-Int. Man., 28, 238-244
• 18. Miron I.M., Gaudin G., Auffert S., Rodmacq B., Schuhl A., Pizzini S., Vogel J., Gambardella P., 2010, Current-driven spin torque induced by the Rashba effect in a ferromagnetic metal layer, Nat. Mater., 9, 230-234
• 19. Newton I., 1687, Philosophiae Naturalis Principia Mathematica: Axiomata, Sive leges motus, Editio tertia aucta et emendata, Londini: apud Guil. & Joh. Innys, Regiae Societatis Typographos
• 20. Ralph D., Stiles M., 2008, Spin transfer torques, J. Magn. Mater., 320, 1190-1216, doi:10.1016/j.jmmm.2007.12.019
• 21. Rashba E., 1960, Properties of semiconducters with an extremum loop. Cyclotran and combi national resonance in a magnetic field perpendicular to the plane of the loop, Sov. Phys. Solid State, 2, 1109-1122
• 22. Shi H., Yang H., Gong G., Wang L., 2011, Determination of the cutterhead torque for EPB shield tunneling machine, Aut. Constr., 20, 1087-1095
• 23. Sluka V., Kaky A., Deac A.M., Burgler D.E., Hertel R., Schneider C.M., 2011, Spin transter torque induced vortex dynamics in Fe/Ag/Fe nanopillars, Journal of Physics D: Applied Physics, 44, 384002, (8pp), doi:10.1088/0953-8984/23/45/456001
• 24. Starzhunskii V.M., 1982, An Advanced Course of Theoretical Mechanics, for Engineering Students, Moscow, Mir Publishers
• 25. Wilczynski M., 2011, Thermopower, figure of merit and spin-transfer torque induced by the temperature gradient in planar tunnel junctions, J. of Physics.: Cond. Matter., 23, 456001 (12pp)
• 26. Yehia H.M., 2003, Kovalevskaya’s integrable case: Ceneralizations and related new results, Reg. Chao. Dyn., 8, 337-348
• 27. Yehia H.M., Elmandouh A.A., 2011, New conditional integrable cases of motion of a rigid body with Kovalevskaya’s configuration, J. of Physics A: Math. and Theor.., 44, 012001 (8pp)