Nonstandard topics in classical mechanics
The proposed course of lectures will cover the parts of classical mechanics that are not included in the standard textbooks and in the courses of theoretical mechanics including:
absolute, relative and conditional integral and tensor invariants, Dirac mechanics, Nambu mechanics, vakonomic mechanics, constrained mechanical systems, nonholonomic mechanics, geometric optimal control theory, forced hybrid mechanical systems, Riemannian and sub Riemannian metrics, geometrical optics.
Students are welcome to suggest other mathematically interesting topics in and around classical mechanics, and I will try to cover these topics in the lectures.
Knowledge of basic topics in classical mechanics, calculus of variations, differential and integral calculus, and tensor analysis is preferred.
absolute, relative and conditional integral and tensor invariants, Dirac mechanics, Nambu mechanics, vakonomic mechanics, constrained mechanical systems, nonholonomic mechanics, geometric optimal control theory, forced hybrid mechanical systems, Riemannian and sub Riemannian metrics, geometrical optics.
Students are welcome to suggest other mathematically interesting topics in and around classical mechanics, and I will try to cover these topics in the lectures.
Knowledge of basic topics in classical mechanics, calculus of variations, differential and integral calculus, and tensor analysis is preferred.
Lecturer
Date
10th September ~ 26th December, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 09:50 - 11:25 | A3-1a-205 | ZOOM 01 | 928 682 9093 | BIMSA |
Reference
[1] H. Poincare, Les Methodes Nouvelles de la Mecanique Celeste}, Tom III, Dover Pub. Inc., N.Y., (1892).
[2] E. Cartan, Lecons sur les invariants integraux, Hermann, Paris, 1922, 210 pp.
[3] P.A.M. Dirac, Generalized Hamiltonian dynamics, Can. J. Math. 2, 129 (1950).
[4] V.T. Filippov, n-Lie algebras, Siberian Math. J., 26:6 (1985), 879-891.
[5] J. Grabowski, G. Marmo, On Filippov algebroids and multiplicative Nambu-Poisson structures, Diff. Geom. Appl., 12:1, (2000), 35-50.
[6] Y. Kosmann-Schwarzbach, From Schouten to Mackenzie: Notes on brackets, J. Geom. Mech., 13:3, (2021), 459-476.
[7] H.J. Rothe and K.D. Rothe, Classical and Quantum Dynamics of Constrained Hamiltonian Systems (World Scientific, Singapore, 2010).
[8] B. Brogliato. Nonsmooth Mechanics, volume 29 of Communications and Control Engineering. Springer London, 1999.
[9] Francesco Bullo and Andrew D. Lewis. Geometric control of mechanical systems, volume 49 of Texts in Applied Mathematics. Springer-Verlag, New York, 2005.
[10] V. V. Kozlov, Dynamical systems X. General theory of vortices, Encyclopaedia Math. Sci., 67, Springer-Verlag, Berlin, 2003, 184 pp.
[11] P.J. Olver, Lectures on Moving Frames, 2011.
[12] A. A. Agrachev, Y. L. Sachkov, Control Theory from the Geometric Viewpoint, 2004
[2] E. Cartan, Lecons sur les invariants integraux, Hermann, Paris, 1922, 210 pp.
[3] P.A.M. Dirac, Generalized Hamiltonian dynamics, Can. J. Math. 2, 129 (1950).
[4] V.T. Filippov, n-Lie algebras, Siberian Math. J., 26:6 (1985), 879-891.
[5] J. Grabowski, G. Marmo, On Filippov algebroids and multiplicative Nambu-Poisson structures, Diff. Geom. Appl., 12:1, (2000), 35-50.
[6] Y. Kosmann-Schwarzbach, From Schouten to Mackenzie: Notes on brackets, J. Geom. Mech., 13:3, (2021), 459-476.
[7] H.J. Rothe and K.D. Rothe, Classical and Quantum Dynamics of Constrained Hamiltonian Systems (World Scientific, Singapore, 2010).
[8] B. Brogliato. Nonsmooth Mechanics, volume 29 of Communications and Control Engineering. Springer London, 1999.
[9] Francesco Bullo and Andrew D. Lewis. Geometric control of mechanical systems, volume 49 of Texts in Applied Mathematics. Springer-Verlag, New York, 2005.
[10] V. V. Kozlov, Dynamical systems X. General theory of vortices, Encyclopaedia Math. Sci., 67, Springer-Verlag, Berlin, 2003, 184 pp.
[11] P.J. Olver, Lectures on Moving Frames, 2011.
[12] A. A. Agrachev, Y. L. Sachkov, Control Theory from the Geometric Viewpoint, 2004
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Andrey Tsiganov currently works at the Department of Computational Physics, Saint Petersburg State University, Russia. His main research interests are integrable and superintegrable systems in classical and quantum mechanics, nonholonomic and vakonomic mechanics, geometry and topology of dynamical systems, see profile at https://www.researchgate.net/profile/Andrey-Tsiganov. He is one of the organizers of the BIMSA Integrable System Seminar, see https://researchseminars.org/seminar/BIMSA-ISS and https://sites.google.com/view/bimsa-iss.