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Basic Principles of Classical Mechanics
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adiabatic invariant analytic angular momentum asymptotic averaged system canonical center of mass coefﬁcients collision completely integrable Consider constant constraints corresponding deﬁned Deﬁnition degrees of freedom denote depend diffeomorphic differential equations dynamics eigenvalues energy English transl equations of motion equilibrium position Example ﬁnite ﬁrst integral ﬁxed ﬂow ﬂuid follows formula frequencies functional F given group G Hamilton’s equations Hamiltonian system inﬁnitely initial conditions invariant tori Lagrange Lagrangian Lagrangian system Lie algebra linear manifold Math momentum mapping n-body problem neighborhood nondegenerate normal form orbits oscillations parameter periodic solutions perturbation phase portrait phase space plane Poincare point masses Poisson Poisson bracket principle Proposition reduced resonance rigid body rotation Russian satisﬁes separatrices smooth function stable sufﬁciently Suppose surface symmetry group symplectic manifold symplectic structure system with Hamiltonian tangent Theorem theory three-body problem tion tonian torus trajectories transformation unperturbed system values variables variation vector ﬁeld velocity zero