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Mathematical Methods of Classical Mechanics
Vladimir I. Arnold
- 01 Jan 1974
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TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
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Abstract: Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid bodies. Part 3 Hamiltonian mechanics: differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
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Citations
Analytical Approximation Methods for the Stabilizing Solution of the Hamilton–Jacobi Equation
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Canonical Structure of Classical Field Theory in the Polymomentum Phase Space
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Riemannian flag manifolds with homogeneous geodesics
TL;DR: In this article, it was shown that among all flag manifolds M = G/K of a simple Lie group G, only the manifold Com(R 2l+2 ) = SO(2l +1)/U(l) of complex structures in R 2l +2, and the complex projective space CP 2l-1 = Sp(l)/U (1) " Sp( l- 1) "Sp(l- 1") admit a nonnaturally reductive invariant metric with homogeneous geodesics.
Stability and chaos in celestial mechanics
Alessandra Celletti
- 01 Jan 2010
TL;DR: In this article, the authors present classical celestial mechanics and its interplay with dynamical systems in a way suitable for advance level undergraduate students as well as postgraduate students and researchers.
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