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 |
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