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1 Generalised coordinates
5 The Lagrangian for a system of particles
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adiabatic invariant amplitude angular momentum angular velocity arbitrary constants axes of inertia axis calculation called canonical transformation central field centre of mass co-ordinates q coefficients collision components consider corresponding degrees of freedom depends Determine effective cross-section ellipse equal equations of motion expressed in terms external field external force finite formula frame of reference frequency friction generalised co-ordinates given gives Hamilton-Jacobi equation Hamilton's equations Hamiltonian Hence homogeneous function inertial frame interaction kinetic energy Lagrange's equations Lagrangian Landau law of conservation linear mechanical system molecule momenta obtain origin parameter particle moves particle of mass path pendulum period perpendicular plane Poisson bracket position potential energy principal axes PROBLEMS PROBLEM quantities radius vector relation resonance respect right-hand side rigid body rotation scattering small oscillations SOLUTION sphere substituting symmetrical system of co-ordinates theoretical physics theory tion variables vertical z-axis zero