Next: MC226 Numerical Linear Algebra
Up: Year 2
Previous: MC224 Vector Calculus
MC225 Dynamics: orbits and oscillations
| Credits: 10 |
Convenor: Dr. M. D. Dampier |
Semester: 2 |
| Prerequisites: |
essential: MC123 |
|
| Assessment: |
Regular coursework: 20% |
One and a half hour exam: 80% |
| Lectures: |
18 |
Classes: |
6 |
| Tutorials: |
6 |
Private Study: |
51 |
| Labs: |
none |
Seminars: |
none |
| Project: |
none |
Other: |
none |
| Total: |
75 |
|
|
Course Description
This course is built around the two classic solvable problems of particle dynamics:
linear oscillations and Keplerian orbits. But the treatment of these specific problems is
designed to introduce general mathematical tools whose use has been found invaluable
elsewhere in dynamics where most problems are not completely solvable.
Aims
The course aims to take the student on from the basic ideas of Newtonian mechanics to a
point where they can confidently apply simple analytic and qualitative methods to the
solution of some key types of problem. The ideas used in the course are developed further
in the modules MC323 Ordinary Differential Equations and MC322 Modelling Physical
Systems.
Objectives
To understand key dynamical concepts - Momentum, Force, Equation of motion, Initial
conditions, Field of force, Kinetic energy, Potential energy, Conservation of energy.
To be able to use the Energy diagram to understand and describe Unbounded motion,
Libration motion, Limitation motion, Equilibrium point, Stable equilibrium, Unstable
equilibrium.
To understand how to linearise an equation of motion and to deal with simple linear
problems - simple harmonic motion, anti-simple harmonic motion, motion with dissipative
forces including damped oscillations.
To be able to draw simple phase space diagrams.
To be able to use vector and coordinate methods to study orbits under the inverse square
law.
To draw information out of first integrals of the equations of motion.
Syllabus
I. Oscillations:
1. Introduction: the 1-dimensional equation of motion.
2. Tool 1: the energy diagram.
3. Tool 2: linearization.
4. Tool 3: phase space.
5. Linear Oscillations.
II. Orbits.
1. Introduction: NewtonÂ’s law of gravitation.
2. Circular orbits.
3. Tool 4: conservation laws.
4. Tool 5: new coordinates.
5. Keplerian orbits.
Reading list
Recommended:
C.D.Collinson & T.Roper,
Particle Mechanics,
Arnold
Although the above book does not quite reflect the spirit of the lectures it is at about the level of
the course and does not contain too much additional material.
Another more comprehensive treatment is in.
D.N.Burghes & A.M.Downs,
Modern Introduction to Classical Mechanics and Control,
Ellis Horwood.
Details of Assessment
The final assessment of this module will consist of 20% coursework and 80% from a
one and a half hour examination during the Summer exam period. The 20% coursework
contribution will come from weekly work. In all there will be five pieces of
coursework.
The examination paper will contain 4 questions with full marks on the paper
obtainable from 3 complete answers.
Next: MC226 Numerical Linear Algebra
Up: Year 2
Previous: MC224 Vector Calculus
Roy L. Crole
10/22/1998