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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
Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling
Yuya Tanizaki,Takayuki Koike +1 more
TL;DR: In this article, the authors apply the Picard-Lefschetz theory to path integrals of quantum mechanics, in order to compute real-time dynamics directly, and demonstrate its computational method in a concrete way by solving three simple examples of quantum quantum mechanics.
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Generalized Kahler manifolds and off-shell supersymmetry
TL;DR: In this paper, the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two-dimensional sigma model was solved.
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Analysis of wave fields by Fourier integral operators and their application for radio occultations
M. E. Gorbunov,Kent B. Lauritsen +1 more
TL;DR: In this paper, the authors derived a closed derivation of the exact phase function of the FIO obtained in the phase matching approach by Jensen et al. and derived a novel FIO algorithm denoted CT2, which is a modification and improvement of FSI.
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Lipid membranes with free edges.
TL;DR: Analytical and numerical solutions to these equations are obtained under the axisymmetric condition and can be used to explain recent experimental results obtained by Saitoh et al.
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Topological mixing with ghost rods.
TL;DR: The ghost rods framework provides a new technique for quantifying chaos and gives insight into the mechanisms that produce chaos and mixing.
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