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Lectures on Celestial Mechanics
TLDR
The three-body problem was studied in this paper, where Covarinace of Lagarangian Derivatives and Canonical Transformation were applied to the problem of estimating the perimeter and the velocity of the system.Abstract:
The Three-Body Problem: Covarinace of Lagarangian Derivatives.- Canonical Transformation.- The Hamilton-Jacobi Equation.- The Cauchy-Existence Theorem.- The n-Body Poblem.- Collision.- The Regularizing Transformation.- Application to the Three-Bdy Problem.- An Estimate of the Perimeter.- An Estimate of the Velocity.- Sundman's Theorem.- Triple Collision.- Triple-Collision Orbits.- Periodic Solutions: The Solutions of Lagrange.- Eigenvalues.- An Existence Theorem.- The Convergence Proof.- An Application to the Solution of Lagrange.- Hill's Problem.- A Generalization of Hill's Problem.- The Continuation Method.- The Fixed-Point Theorem.- Area-Preserving Analytic Transformations.- The Birkhoff Fixed-Point Theorem.- Stability: The Function-Theoretic Center Problem.- The Convergence Proof.- The Poincare Center Problem.- The Theorem of Liapunov.- The Theorem of Dirichlet.- The Normal Form of Hamiltonian Systems.- Area-Preserving Transformations.- Existence of Invariant Curves.- Proof of Lemma.- Application to the Stability Problem.- Stability of Equilibrium Solutions.- Quasi-Periodic Motion and Systems of Several Degrees of Freedom.- The Recurrence Theorem.read more
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Nonlinear stability of fluid and plasma equilibria
TL;DR: The Liapunov method for establishing stability has been used in a variety of fluid and plasma problems, such as MHD, multilayer quasigeostrophic flow, adiabatic flow and the Poisson-Vlasov equation.
Stability in dynamical systems
Abstract: Stability in dynamical systems subject to some law of force is considered. This leads to a set of differential equations which govern the motion. (AIP)
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The Lorenz attractor exists
Warwick Tucker,Warwick Tucker +1 more
TL;DR: In this article, it was shown that the Lorenz equations support a strange attractor, and that the attractor persists under small perturbations of the coefficients in the underlying differential equations.
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Geometric numerical integration illustrated by the Störmer-Verlet method
TL;DR: In this article, the authors present a cross-section of the recent monograph by Newton-Stormer-Verlet-leapfrog method and its various interpretations, followed by a discussion of geometric properties: reversibility, symplecticity, volume preservation, and conservation of first integrals.