Proceedings of the International Conference on Geometry, Integrability and Quantization

The Two Apparently Different But Hiddenly Related Euler Achievements: Rigid Body and Ideal Fluid. Our Unifying Going Between: Affinely-Rigid Body and Affine Invariance in Physics

Jan J. Sławianowski

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Abstract

Reviewed are ideas underlying our concept of affinely-rigid body. We do this from the perspective of the Leonhard Euler two main achievements, known under his name: the mechanics of rigid body and the dynamics of incompressible ideal fluid. But we formulate the theory which is somehow placed between those two models. Our scheme is a finite-dimensional dynamical system, but admitting deformative degrees of freedom. We also stress the connection with the general idea of affine invariance in physics.

Article information

Source
Proceedings of the Sixteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Andrei Ludu and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2015), 36-72

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815736

Digital Object Identifier
doi:10.7546/giq-16-2015-36-72

Mathematical Reviews number (MathSciNet)
MR3363837

Zentralblatt MATH identifier
1352.37158

Citation

Sławianowski, Jan J. The Two Apparently Different But Hiddenly Related Euler Achievements: Rigid Body and Ideal Fluid. Our Unifying Going Between: Affinely-Rigid Body and Affine Invariance in Physics. Proceedings of the Sixteenth International Conference on Geometry, Integrability and Quantization, 36--72, Avangard Prima, Sofia, Bulgaria, 2015. doi:10.7546/giq-16-2015-36-72. https://projecteuclid.org/euclid.pgiq/1436815736


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