Dynamical Systems, Volume 31. Ordinary differential equations and smooth dynamical systems by D.V. Anosov, V.I. Arnold (eds.). 2. Ergodic theory with applications to dynamical systems an d statistical mechanics by Ya. G. Sinai (ed.). 3. [without special title]. 4. S ymplectic geometry and its applications by V.I. Arnold, S.P. Novikov (eds.). |
Contents
Basic Principles of Classical Mechanics | 1 |
Lagrangian Mechanics | 9 |
Hamiltonian Mechanics | 20 |
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adiabatic invariant analytic angular momentum asymptotic averaged system axis canonical center of mass coefficients collision configuration Consider constant constraints coordinates corresponding defined degrees of freedom denote depend diffeomorphic differential equations dynamics eigenvalues energy English transl equations of motion equilibrium position Example F₁ fixed follows force formula frequencies functional F group G H₁ Hamilton's equations Hamiltonian system initial conditions invariant tori Lagrange Lagrangian Lagrangian system Lie algebra linear m₁ manifold Math momentum mapping n-body problem neighborhood nondegenerate normal form orbits oscillations parameter periodic solutions perturbation phase space plane Poincaré point masses Poisson Poisson bracket principle Proposition reduced resonance rigid body rotation Russian separatrices smooth function stable Suppose surface symmetry group symplectic structure system with Hamiltonian t₁ t₂ tangent Theorem theory three-body problem tion torus trajectories transformation unperturbed system values variables variation vector field velocity zero