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Basic Principles of Classical Mechanics
Topological and Geometrical Obstructions to Complete
27 other sections not shown
adiabatic invariant analytic angular momentum asymptotic averaged system axis called canonical center of mass coefficients collision commutative completely integrable configuration Consider const constant constraints convergence coordinate change corresponding curves defined degrees of freedom denote depend diffeomorphic differential equations domain eigenvalues energy equations of motion equilibrium position Example exists finite fixed follows formula frequencies given group G Hamilton's equations Hamiltonian system independent initial conditions invariant tori Lagrange Lagrangian Lagrangian system Lemma Lie algebra linear momentum mapping n-body problem neighborhood nondegenerate nonresonant normal form obtain orbits oscillations parameter pendulum 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 terms of order Theorem theory three-body problem tion tonian torus trajectories transformation unperturbed values variation vector field zero