Classical mechanics of a breathing top. (English) Zbl 0607.70006
We develop the classical mechanics of a breathing top and consider the left- and right-invariant actions on the configurations space SL(n,R). This model is compared with the affinely-rigid body, based on GL(n,R). Applications of the breathing top can be found in the theory of elasticity and hydromechanics.
MSC:
70E05 | Motion of the gyroscope |
22E70 | Applications of Lie groups to the sciences; explicit representations |
70G45 | Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics |
References:
[1] | Green, A. E.; Adkins, J. E., Large elastic deformations (1960), Clarendon Press: Clarendon Press Oxford · Zbl 0090.17501 |
[2] | Leach, P. G., J. Math. Phys., 21, 300 (1980) · Zbl 0451.70020 |
[3] | Noll, W.; Tupin, R. A.; Wang, C. C., Continuum theory of inhomogeneities in simple bodies (1968), Springer-Verlag: Springer-Verlag New York · Zbl 0167.54204 |
[4] | Seredyńska, M., Bull. Acad. Polon. Sci., 23, 445 (1975) |
[5] | S[lstrok]awianowski, J. J., Arch. Mechanics, 26, 569 (1974) · Zbl 0307.73003 |
[6] | S[lstrok]awianowski, J. J., Int. J. Theor. Phys., 12, 271 (1975) · Zbl 0351.70014 |
[7] | S[lstrok]awianowski, J. J., Rep. Math. Phys., 10, 219 (1976) · Zbl 0352.70004 |
[8] | S[lstrok]awianowski, J. J., IFTR Reports, 1st Polish-Swedish Conference on Micropolar Elasticities, Jab[lstork]onna 1977 (1979), Warsaw |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.