20 credits at level HE5
This module aims to apply the mathematical methods and vector analysis studied in Mathematical Methods 2 (MAS1008) and Vector Analysis (MAS2507) to problems in particle dynamics. The module introduces the concept of mathematical modelling and provides an introduction to the broad field of classical applied mathematics. The classical applied mathematics area may be pursued at Level 3 with the modules Fluid Dynamics (MAS3013) and Differential Equations and Applications (MAS3014). Also, the module provides a thorough background for students intending to teach Applied Mathematics at advanced level.
Motion of a Particle in a Straight Line
Resisted Motion of a Particle in a Straight Line
Two-Dimensional Motion of a Particle: Projectiles
Projectiles: Parabola of Safety and Applications
Coefficient of Restitution: Bouncing Projectiles
Circular Motion of a Particle: Polar Coordinates
Connected Particles and Friction Forces
Conservation of Energy and Applications
Motion of a Particle in Three-Dimensions
Variable Mass and Applications
Students will be given printed notes. About two-thirds of class time will be formal lectures, the remainder being supervised tutorial work. Directed student centred learning will be encouraged throughout the course.
Two pieces of coursework will be set, each to be completed by a prescribed date in the students’ own time. There will be a formal closed-book examination of 2¼ hours duration at the end of the module. The weighting of the two components of assessment is as follows:
Coursework: 30% Examination: 70%
when you have successfully completed this module you will:
to demonstrate that you have achieved the learning outcome you will:
|1.||Understand the creative process and methods of solution of models for two-dimensional particle dynamics using rectangular coordinates.||Demonstrate the ability to model problems in two-dimensional particle dynamics using rectangular coordinates. Demonstrate an ability to solve the governing differential equations of the model.|
|2.||Understand the creative process and methods of solution of models for two-dimensional particle dynamics using polar coordinates.||Demonstrate the ability to model problems in two-dimensional particle dynamics using polar coordinates. Demonstrate an ability to solve the governing differential equations of the model.|
|3.||Understand the effects of tension and friction forces. Understanding the effects of variable mass.||Demonstrate an ability to incorporate tension and friction forces into the mathematical model. Solve problems involving variable mass.|
|4.||Understand the creative process and methods of solution of models for three-dimensional constrained particle dynamics.||Demonstrate the ability to model problems in three-dimensional constrained particle dynamics. Demonstrate an ability to solve the governing differential equations of the model.|
Your achievement of the learning outcomes for this module will be tested as follows:
|Description||Assignment on modelling two-dimensional particle dynamics applications using rectangular and polar coordinates. Assignment on modelling two- and three-dimensional (constrained) particle motion.||2¼ hour examination covering the syllabus described above.|
Before taking this module you must have successfully completed the following:
and/or be taking the following corequisite modules:
You cannot take this module if you are taking or have taken:
Chorlton, Frank. Textbook of Dynamics, Ellis Horwood, 1989.
Chester, W. Mechanics, Chapman and Hall, 1979.
Dyke P. & Whitworth R. Guide to Mechanics, Macmillan, 1992.
Prasad, G. Textbook of Dynamics, Navyug Publishers and Distributors 2008
Smith, P and Smith, R.C. Mechanics, 1990.
|Host Subject Group:|
|User Name||Date Accessed||Action|