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classical-mechanics newton-s-laws-of-motion history-of-classical-mechanics space time mass force energy momentum-2 lagrange-s-equation dynamics-physics kinematics applied-mechanics celestial-mechanics continuum-mechanics statistical-mechanics sir-isaac-newton leonhard-euler jean-le-rond-d-alembert alexis-clairaut joseph-louis-lagrange pierre-simon-laplace william-rowan-hamilton heinrich-hertz symplectic-manifold coordinate-space phase-space equation quantum-mechanics kinetic-energy potential-energy differential-equation generalized-coordinates conservation-of-energy kinetic-3 gradient lagrangian broken-symmetry symmetry symplectic-geometry conservation-law degrees-of-freedom-physics-and-chemistry integrable-system canonical-coordinates cartesian-coordinate-system coordinates angular-momentum legendre-transformation fiber-bundle level-set jet-bundle cotangent-space symplectic-vector-space poisson-algebra moyal-bracket poisson-bracket lie-algebra probability-distribution wigner-quasi-probability-distribution smooth-function hamiltonian-vector-field vector-field symplectic-vector-field integral-curve canonical-transformation liouville-equation volume-form kolmogorov-arnold-moser-theorem-2 chaos-theory-3 dynamical-systems-theory quadratic-form configuration-space kinetic-term riemannian-manifold pseudo-riemannian-manifold metric-mathematics hamilton-jacobi-equation geodesic rank-mathematics sub-riemannian-manifold heisenberg-group associative-algebra commutativity unital real-number state-functional-analysis continuous-function-topology linear-functional topological-space nambu-mechanics particle electromagnetic-2 international-system-of-units electric-charge electrical-potential magnetic-potential gauge-fixing cambridge-university-press vladimir-arnold ralph-abraham

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