Foundations Of Mechanics

By R. Abraham. 2019

2,676 citations recorded by the source corpus.

Introduction Foreward by Tudor Ratiu and Richard Cushman Preliminaries Differential Theory Calculus on Manifolds Analytical Dynamics Hamiltonian and Lagrangian Systems Hamiltonian Systems with Symmetry Hamiltonian-Jacobi Theory and Mathematical Physics An Outline of Qualitative Dynamics Topological Dynamics Differentiable Dynamics Hamiltonian Dynamics Celestial Mechanics The Two-Body Problem The Three-Body Problem.

Subfields: Atomic and Molecular Physics, and Optics, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bbdb0b63eb59c30c57042f39a6348137595aa3f1

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. D. Vogan
2. Juan-Pablo Ortega
3. P. Ballard
4. Jerrold E. Marsden
5. Nguyen Tien Zung
6. Fumin Zhang
7. Alessio Figalli
8. Wang Sang Koon

In Control and Systems Engineering

1. Jerrold E. Marsden
2. A. J. van der Schaft
3. Guido Blankenstein
4. Naomi Ehrich Leonard
5. Fumin Zhang
6. D. Vogan
7. Juan-Pablo Ortega
8. P. Ballard

In Statistical and Nonlinear Physics

1. G. Contreras
2. Jerrold E. Marsden
3. Guido Blankenstein
4. J. Ramis
5. A. J. van der Schaft
6. Naomi Ehrich Leonard
7. Fumin Zhang
8. Juan J. Morales-Ruiz

Citations in the corpus

• Symmetry and reduction in implicit generalized Hamiltonian systems (2001, methodology): “result, and is a generalization of the classical reduction theorems for (explicit) symplectic and Poisson Hamiltonian systems described in [ 1 , 7, 9, 12].”
• A Minimizing Property of Lagrangian Solution (2001, background): “It is easy to verify that the energy E = 1 |˙ x| 2 −| x| −1 and the angular momentum G = x × ˙ x are constants of the motion (see [ 1 ] or [3]).”
• REDUCTION, RECONSTRUCTION, AND SKEW-PRODUCT DECOMPOSITION OF SYMMETRIC STOCHASTIC DIFFERENTIAL EQUATIONS (2007, background): “Symmetries have historically played a role of paramount importance in the study of dynamical systems in general (see [GS85, GS02, ChL00], and references therein) and of physical, mechanical, and Hamiltonian systems in particular (see for instance [ AM78 , MR99, OR04] for general presentations of the”
• Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊2 (2009, background): “the symplectic form !. We refer the reader to [ 1 , 6] for more details about the notions of symplectic geometry introduced above.”
• Dynamical Systems, the Three-Body Problem and Space Mission Design (2009, methodology): “For a Hamiltonian approach, see Abraham and Marsden [1978] or Meyer and Hall [1992].”