## Mechanics |

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### Contents

THE EQUATIONS OF MOTION | 1 |

5 The Lagrangian for a system of particles | 8 |

8 Centre of mass | 16 |

Copyright | |

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### Common terms and phrases

amplitude angle angular momentum angular velocity arbitrary constants axes of inertia axis called canonical transformation central field centre of mass closed system 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 law of conservation linear mechanical system momenta obtain origin parameter parametric resonance particle moves particle of mass path period perpendicular plane Poisson bracket position potential energy principal axes 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 z-axis zero