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 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]
|
Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2022/23, Available to all students (SV1)
|
Quota: 48 |
| Course Start |
Semester 1 |
| Course Start Date |
19/09/2022 |
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) | | 2:00 | | | 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 co-ordinate 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: |
Course secretary | Miss Emma Summers
Tel: (0131 6)51 7524
Email: |
|
|
University Homepage