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Basic Principles of Classical Mechanics
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adiabatic invariant analytic angular momentum asymptotic averaged system axis called canonical center of mass coefficients collision completely integrable configuration Consider const constant constraints convergence Corollary corresponding defined degrees of freedom denote depend diffeomorphic differential equations domain eigenvalues equations of motion equilibrium position Euler Example exists finite fixed follows force formula frequencies functional F given group G Hamilton's equations Hamiltonian system independent initial conditions invariant tori Lagrange Lagrange's equations Lagrangian Lagrangian system Lemma Lie algebra linear manifold mechanical system momentum mapping n-body problem neighborhood nondegenerate normal form orbits oscillations parameter periodic solutions perturbation phase portrait phase space plane Poincare point masses Poisson bracket potential principle Proposition reduced resonance rigid body rotation satisfies separatrices smooth function Suppose surface symmetry group symplectic structure system with Hamiltonian terms of order Theorem theory three-body problem tion torus trajectories transformation unperturbed system values variables variation vector field zero