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Semester 1

Introductory Dynamics (PHYS08052)

Subject

Physics and Astronomy

College

SCE

Credits

10

Normal Year Taken

2

Delivery Session Year

2022/2023

Pre-requisites

Course Summary

The course teaches the principles of Newtonian mechanics along with the necessary mathematical tools of differential equations. It focuses on deriving results from first principles and aims at strengthening the student's problem-solving skills. It provides a suitable preparation for JH courses, in particular Lagrangian dynamics, Electromagnetism and relativity, and for Principles of quantum mechanics.

Course Description

- Introduction to dynamics: Newton's laws, examples of forces, conservative and non-conservative, kinetic and potential energy, energy conservation, momentum conservation, and their origin in translational symmetry in one dimension. [2] - Introduction to differential equations: classification, initial conditions, first-order equations, existence and uniqueness theorem, separable equations and substitution, first-order linear equations and integrating factors. [3]- Simple harmonic motion, equation of motion, kinetic and potential energy, turning points, period. Simple pendulum (in the small angle approximation). Hooke's law. Large oscillations: oscillatory motion in a general one-dimensional potential. [2]- Damped harmonic oscillator, principle of superposition. Homogeneous second-order equations with constant coefficients. Forced damped harmonic oscillator. Inhomogeneous second-order equations (with constant coefficients). [3]- Coupled oscillators, normal models (requires knowledge of eigenvalues and eigenfunctions), transverse and longitudinal oscillations, coupled pendulums, double pendulum. [2]- Second and higher order equations, existence and uniqueness, reduction of order, trial functions. Variable mass problems, the mass accretion equation. [2]- Introduction to several variable calculus: partial derivatives, change of variables, polar cylindrical and spherical polar co-ordinates, Jacobians. [2]- Dynamics in two and three dims: Newton's Laws in vector form, conservative forces, momentum and energy conservation in three dimensions and their origin in translational symmetry. Cartesian basis, polar basis, angular momentum conservation and rotational symmetry. Resisted motion in 2 dimensions. [3]- Central forces and motion in a plane, angular momentum conservation, effective potential, closed and open orbits. The orbit equation and its solutions. Kepler's laws. [2]

Assessment Information

Written Exam 80%, Coursework 20%, Practical Exam 0%

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