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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 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 given group G Hamilton's equations Hamiltonian system independent initial conditions invariant tori Kepler's problem Lagrange Lagrangian Lagrangian system Lie algebra linear manifold mechanical system metric momentum mapping n-body problem neighborhood nondegenerate normal form obtain orbits oscillations parameter path periodic solutions perturbed system phase portrait phase space plane Poincare point masses Poisson bracket potential Proposition reduced resonance rigid body rotation satisfies separatrices smooth function Suppose surface symmetry group symplectic structure system with Hamiltonian tangent terms of order Theorem theory three-body problem tion torus trajectories transformation unperturbed values variables variation vector field zero