Geometric Mechanics and Symmetry The Peyresq Lectures [Paperback]

The lectures in this 2005 book are intended to bring young researchers to the current frontier of knowledge in geometrical mechanics and dynamical systems.Geometric mechanics lies on the border of pure and applied mathematics and incorporates such disciplines as differential geometry, Hamiltonian mechanics and integrable systems. The editors organised a summer school on Geometric Mechanics and Symmetry from which the main courses have been written up and published here. The book was written with a significant input from the participants at the conference. This means that the lecture notes are thoroughly geared towards the needs of a graduate student and take great care to explain concepts at the correct level.Geometric mechanics lies on the border of pure and applied mathematics and incorporates such disciplines as differential geometry, Hamiltonian mechanics and integrable systems. The editors organised a summer school on Geometric Mechanics and Symmetry from which the main courses have been written up and published here. The book was written with a significant input from the participants at the conference. This means that the lecture notes are thoroughly geared towards the needs of a graduate student and take great care to explain concepts at the correct level.Geometric mechanics borders pure and applied mathematics and incorporates such disciplines as differential geometry, Hamiltonian mechanics and integrable systems. The source of this collection is the summer school on Geometric Mechanics and Symmetry organized by James Montaldi and Tudor Ratiu. Written with significant input from the participants at the conference, these lecture notes are geared towards fulfilling the needs of graduate students through their attention to detail.1. Stability in Hamiltonian systems: applications to the restricted three-body problem K. R. Meyer, B. Rink and T. Tuwankotta; 2. A crash course in geometric mechanics T. S. Ratiu, E. Sousa Dias, L. Sbano, G. Terra and R. Tudoran; 3. l+