Lecture_Handout - Part IB Physics B Classical Dynamics and...

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Unformatted text preview: Part IB Physics B Classical Dynamics and Fluids S.F. Gull University of Cambridge Department of Physics Lent Term 2009 Synopsis Coordinate systems . Rotating frames, fictitious forces, Coriolis force, centrifugal force. Examples. Review of Newtonian mechanics . Linear and angular momentum, energy. Galilean transformation. Orbits . Central force field, Kepler’s 2nd Law. Effective radial equa- tion. Power-law force fields. Nearly circular orbits. Inverse square orbits, shape of orbit, time in orbit, Kepler’s 1st and 3rd laws. Hyper- bolic orbits. Rigid body dynamics . Principles. Angular velocity and momentum. Moment of Inertia tensor, and ellipsoid. Free motion of a symmetrical top: (a) Poinsot’s treatment, invariable plane, polhodes and herpol- holdes, space-cone, body-cone; (b) Euler’s equations. Asymmetrical top. Forced precession, nutation. Small oscillations, normal modes . N-parameter systems, normal modes, orthogonality, relation to eigenvalue theory, energy, standing wave systems. Elasticity . Stress, strain, elastic modulus, moduli (Young’s, bulk, shear) and Poisson’s ratio for an isotropic material. Energy. Simple examples, bending beams, Euler strut. 1 Books The course is awkwardly served with books. The choice seems to be between essentially IA-ish books which cover much of the area but in an elementary way, or more comprehensive treatises on specific areas of which only the introductory chapters are relevant. The former include: French and Ebison Introduction to Classical Mechanics: Particle dynamics, orbits, elementary rigid body dynamics. French Vibrations and Waves: Normal modes. More comprehensive are Symon Mechanics: Kibble Classical Mechanics: Landau and Lifshitz Vol. 1 – Mechanics: All of these deal with rigid body mechanics at about the right level; in places they use Lagrangian methods, outside the scope of Dynamics I. For elasticity Feynman Lectures on Physics, Vol.2: Two useful chapters. Bhatia and Singh Mechanics of Deformable Media: At about the right level (? too much algebra). Landau and Lifshitz Vol. 7 – Theory of Elasticity: Comprehensive, but probably a bit indigestible. Bullen and Bolt Introduction to the Theory of Seismology: For elastic waves, propagation, reflection etc, and use in geophysics (the major area of application). Riley : Mathematical Methods for the Physical Sciences. Useful for matrices, normal modes. 2 Contents 1 Mathematics — Review 6 1.1 Coordinate systems . . . . . . . . . . . . . . . . . . . . . 6 1.2 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.1 Geometrical view . . . . . . . . . . . . . . . . . . 7 1.3.2 Orthogonal matrices . . . . . . . . . . . . . . . . 7 1.3.3 Tensors . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.4 Eigen vectors, eigen values . . . . . . . . . . . . . 8 1.3.5 Quadratic forms . . . . . . . . . . . . . . . . . . . 9 1.4 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . .....
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Lecture_Handout - Part IB Physics B Classical Dynamics and...

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