Gwybodaeth Modiwlau
Module Identifier
MP25710
Module Title
ADVANCED DYNAMICS
Academic Year
2011/2012
Co-ordinator
Semester
Semester 2
Pre-Requisite
Other Staff
Course Delivery
| Delivery Type | Delivery length / details |
|---|---|
| Lecture | |
| Practical |
Assessment
| Assessment Type | Assessment length / details | Proportion |
|---|---|---|
| Semester Exam | 2 Hours Semester exam | 100% |
| Supplementary Exam | 2 Hours Supplementary exam | 100% |
Learning Outcomes
On successful completion of this module students should be able to:
Use dimensional analysis to simplify problems in Applied Mathematics.
Predict the motion of particles in non-inertial frames of reference.
Model mechanical systems using Lagrange’s equations.
Apply the Euler-Lagrange equations to solve optimization problems.
Aims
The module has two aims: to introduce advanced topics in mechanics, based on the classical work of Newton, Euler, and Lagrange, that will allow students to predict the dynamics of physically important systems; and to improve students’ skills in Applied Mathematics, by deepening their understanding of the mathematical modelling process.
Brief description
Starting from Newton’s laws of motion, the course will develop the techniques necessary to study systems of interacting particles in different frames of reference. It will describe Lagrange’s generalization of Newton’s equations, which allow a simpler treatment of many problems, and a derivation of the Euler-Lagrange equations in the calculus of variations.
Content
Dimensional analysis, scaling arguments.
Newtonian mechanics of systems of particles; kinematics; 2-body problem; conservation laws; rotating frames; examples.
Lagrangian formulation of mechanics; generalized coordinates; examples.
Review of Taylor’s Theorem. Calculus of variations; Euler-Lagrange equations; variational problems; examples.
Newtonian mechanics of systems of particles; kinematics; 2-body problem; conservation laws; rotating frames; examples.
Lagrangian formulation of mechanics; generalized coordinates; examples.
Review of Taylor’s Theorem. Calculus of variations; Euler-Lagrange equations; variational problems; examples.
Module Skills
| Skills Type | Skills details |
|---|---|
| Application of Number | Necessary throughout |
| Communication | Written answers to exercises must be clear and well-structured. Good listening skills are essential to progress in this course. |
| Improving own Learning and Performance | Students will be expected to develop their own approach to time-management in their attitude to the completion of work on time, and in doing the necessary preparation between lectures. |
| Information Technology | Work will be set which requires the use of library facilities |
| Personal Development and Career planning | Completion of tasks (exercise sheets) to set deadlines will aid personal development. |
| Problem solving | An exercise sheet will be set for each of the exercise classes and selected exercises marked. |
| Research skills | Students will be expected to use the written resources to find supplementary material. |
| Subject Specific Skills | Broadens student knowledge of topics in applied mathematics. |
| Team work | Students will be encouraged to work together on questions during the exercise classes. |
Notes
This module is at CQFW Level 5