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3 Galileos relativity principle | 5 |
5 The Lagrangian for a system of particles | 11 |
8 Centre of mass | 17 |
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amplitude angle angular momentum angular velocity arbitrary constants axes of inertia axis called canonical transformation central field centre of mass co-ordinates q coefficients collision components corresponding degrees of freedom depends Determine differential effective cross-section ellipse equations of motion external field external force Əqi finite formula frame of reference frequency generalised co-ordinates given gives Hamilton-Jacobi equation Hamilton's equations Hamiltonian Hence homogeneous function I₁ inertial frame interaction kinetic energy Lagrange's equations Lagrangian law of conservation linear m₁ M₂ mechanical system mi+m2 molecule momenta obtain p₁ parameter particle moves particle of mass path perpendicular plane Poisson bracket position potential energy PROBLEMS PROBLEM quantities radius vector resonance respect right-hand side rigid body rmin rotation scattering small oscillations SOLUTION sphere substituting symmetrical system of co-ordinates tion total time derivative variables vertical x-axis z-axis zero