Abstract
Serbest bir katı cismin dönme hareketinde, eylemsiz bir koordinat sistemine göre sabit olan açısal momentum vektörü, cismin kütle merkezine sabitlenmiş koordinat sisteminden bakıldığında periyodik bir harekete sahiptir. Fakat açısal momentum vektörü bir periyodluk hareketini tamamladığında cisim bir bütün olarak periyodik bir hareket sergilememektedir. Robot ve uydu hareketlerinde önemli düzeltmeler gerektiren bu hareket tarzı analiz edilerek, simetrik bir topaç için cismin net dönme miktarı alternatif bir yaklaşımla türetilmiştir
References
- Goldstein, H., Poole, C. and Safko, J., “Classical Mechanics”, Addison-Wesley, 161, (2002)
- Landau, L. D. and Lifshitz, E. M., “Mechanics”, Bristol, Pergamon, (1960)
- Levi, M., “Geometric Phases in the Motion of Rigid Bodies”, Arch. Rational Mech. Anal, 122, 213-229, (1993), ( Önbasım olarak 1990 )
- Marsden, J. E., Montgomery, R. and Ratiu, T., “Reduction, Symmetry and Berry’s Phase in Mechanics”, Memoirs of AMS, 436, 1-110, (1990)
- Montgomery, R., “How Much Does the Rigid Body Rotate? A Berry’s Phase from the 18th Century”, Am. J. Phys., 59(5), 394-398, (1990)
- Teğmen, A., “Rigid Body Phase Formula in terms of Poincare-Cartan Invariant Action Form”, (Basım için hazırlanmaktadır). Nambu, Y., “Generalized Hamiltonian Dynamics”, Phys. Rev. D, 7, 2405-2412, (1973)
- Berry, M. V., “Quantal Phase Factors Accompanying Adiabatic Changes”, Proc. R. Soc. Lond. A, 392, 45-57, (1984)
- Hannay, J. H., “Angle Variable Holonomy in Adiabatic Excursion of an Integrable Hamiltonian”, J. Phys. A, 18, 221-230, (1985)
Abstract
In the rotational motion of a free rigid body, the angular momentum vector which is constant with respect to an inertial frame has a periodic motion when viewed from the frame fixed at the center of mass of the body. But when the angular momentum vector completes its one-period motion, the body as a whole does not exhibit a periodic motion. This kind of motion which generates important corrections in the motions of robots and satelites has been analyzed and, for a symmetrical top, the net amount of rotation of the rigid body has been derived via an alternative approach
References
- Goldstein, H., Poole, C. and Safko, J., “Classical Mechanics”, Addison-Wesley, 161, (2002)
- Landau, L. D. and Lifshitz, E. M., “Mechanics”, Bristol, Pergamon, (1960)
- Levi, M., “Geometric Phases in the Motion of Rigid Bodies”, Arch. Rational Mech. Anal, 122, 213-229, (1993), ( Önbasım olarak 1990 )
- Marsden, J. E., Montgomery, R. and Ratiu, T., “Reduction, Symmetry and Berry’s Phase in Mechanics”, Memoirs of AMS, 436, 1-110, (1990)
- Montgomery, R., “How Much Does the Rigid Body Rotate? A Berry’s Phase from the 18th Century”, Am. J. Phys., 59(5), 394-398, (1990)
- Teğmen, A., “Rigid Body Phase Formula in terms of Poincare-Cartan Invariant Action Form”, (Basım için hazırlanmaktadır). Nambu, Y., “Generalized Hamiltonian Dynamics”, Phys. Rev. D, 7, 2405-2412, (1973)
- Berry, M. V., “Quantal Phase Factors Accompanying Adiabatic Changes”, Proc. R. Soc. Lond. A, 392, 45-57, (1984)
- Hannay, J. H., “Angle Variable Holonomy in Adiabatic Excursion of an Integrable Hamiltonian”, J. Phys. A, 18, 221-230, (1985)
Details
| Other ID | JA22DM88AU |
|---|---|
| Authors | |
| Publication Date | December 1, 2005 |
| Submission Date | December 1, 2005 |
| Published in Issue | Year 2005 Volume: 7 Issue: 2 |