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Analysis on Manifolds
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algebra angle variables angular momentum bijection boundary bundle calculate canonical flow canonical transformation Cartesian clocks compact components constants of motion coordinate system cos2 cosh2 covariant curve defined Definition dense depends diffeomorphism differential eigenvalues energy equations of motion example exist extended phase space Figure finite force frequencies function global gxfi Hamiltonian Hamiltonian vector fields Hence implies independent constants infinity integrable invariance group inverse image Lie derivative linear Lorentz transformation manifold mapping mass mathematical matrix measure metric Minkowski space momenta neighborhood open sets open subset orbits oscillator particles perturbation phase space physics plane Poincare group point q point transformation Poisson brackets potential Problem Proof region relativistic Remarks restricted rotating Show sin2 solution stability structure submanifold tangent space tensor field theorem theory time-evolution topology Tq(M trajectories vanishes vector field velocity zero