Undergraduate Course: Introductory Dynamics (PHYS08052)
Course Outline
School  School of Physics and Astronomy 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 8 (Year 2 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
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 problemsolving 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 nonconservative, 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, firstorder equations, existence and uniqueness theorem, separable equations and substitution, firstorder 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 onedimensional potential. [2]
 Damped harmonic oscillator, principle of superposition. Homogeneous secondorder equations with constant coefficients. Forced damped harmonic oscillator. Inhomogeneous secondorder 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 coordinates, 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]

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2024/25, Available to all students (SV1)

Quota: 48 
Course Start 
Semester 1 
Course Start Date 
16/09/2024 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 22,
Feedback/Feedforward Hours 2,
Summative Assessment Hours 2,
Revision Session Hours 3,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
47 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
20% Coursework
80% Examination 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)  Introductory Dynamics Dec Exam  2:120   Resit Exam Diet (August)   2:00  
Learning Outcomes
 Understand the foundational principles of Newtonian dynamics and how they relate to broader physical principles.
 Understand in detail energy, momentum and angular momentum conservation, and their relation to symmetry.
 Develop a working knowledge of the elements of several variable calculus, and the usage of different coordinate systems.
 Be able to formulate and solve elementary dynamical problems involving motion in potentials, simple harmonic motion, and coupled oscillators, in one, two and three dimensions.
 Devise and implement a systematic strategy for solving a simple problem by breaking it down into its constituent parts.
 Use the experience, intuition and mathematical tools learned from solving physics problems to solve a wider range of unseen problems.
 Resolve conceptual and technical difficulties by locating and integrating relevant information from a diverse range of sources.

Reading List
RD Gregory, Classical Mechanics (Cambridge)  first choice
KF Riley and MP Hobson, Essential Mathematical Methods for the Physical Sciences (CUP)
GR Fowles and GL Cassiday, Analytical Mechanics (Saunders)
TWB Kibble, FH Berkshire, Classical Mechanics (Imperial College Press)
WD McComb, Dynamics and Relativity (Oxford)
KF Riley and MP Hobson, Essential Mathematical Methods for the Physical Sciences (CUP)

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  IntDyn 
Contacts
Course organiser  Prof Arjun Berera
Tel: (0131 6)50 5246
Email: ab@ph.ed.ac.uk 
Course secretary  Mr Kieran Brodie
Tel:
Email: v1kbrodi@exseed.ed.ac.uk 

