Course Archives Theoretical Statistics and Mathematics Unit | ||||||||
Course: Classical Mechanics Level: Undergraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus: i) Space, time, force and inertial mass; Newtons three laws of motion in differential vector form; Projectile motion with and without air resistance; frictional forces and tension forces; Gravitational forces. ii) Rotational Motion of a particle or system of particles about an axis; Uniform circular motion and centripetal force; Torque; Center of Mass; Linear momentum, Angular momentum and their conservation. Static and dynamic equilibrium. iii) Work-energy theorem; Kinetic energy and potential energy; potential for conservative forces; Work done by non-conservative forces; Principle of conservation of mechanical energy. iv) Oscillations and Hookes Law; Simple Harmonic Motion in one and two dimensions; Damped Oscillations; Driven damped oscillations; Resonances. v) Calculus of variations and Euler-Lagrange equations; Generalized co-ordinates as degrees of freedom; The Lagrangian and the action; The principle of the Stationarity of the action; Lagranges Equations for constrained and unconstrained systems; Lagrange multiplier method. Noethers theorem and re-visiting the Conservation of linear momentum, angular momentum and mechanical energy vi) The Central Force problem; Centre-of-Mass and relative co-ordinates; Motion in the Centre of Mass frame; Conservation of angular momentum; Bounded and unbounded Keplerian orbits. vii) Rigid Bodies: The rotation problem about a fixed axis; the Angular momentum; The inertia tensor; Principal inertial axis; the Eigenvalue equation; The spinning top problem. Viii) The Hamiltonian formalism; phase-space co-ordinates; Legendre transformation and construction of the Hamiltonian from the Lagrangian; Hamiltons equation of motion; Liouvilles theorem for the phase-space; if time permits, the instructor may feel free to discuss topics like Poisson brackets, orbits in phase space, etc. ix) Any other special topics are left to the discretion of the instructor. Reference Texts: (a) Classical Mechanics - J. R. Taylor. (b) Classical Dynamics of Particles and Systems - S. T. Thornton, J. B. Marion. (c) Classical Mechanics (3rd edition) - H. Goldstein, C. Poole, J. Safko. (d) Fundamentals of Physics - R. Resnick, D. Halliday and J. Walker. Evaluation:
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Midterm
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