MP2B: Dynamics (U03870)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : PHY-2-MP2B

The course provides an introduction to Mathematical Physics and training in the associated concepts and mathematical skills. The strong connections between Mathematics and Physics are highlighted within the arena of Classical Dynamics. Beginning from Newton's second law as a differential equation, key physical quantities such as energy and angular momentum are identified and defined mathematically. The role of conservation laws is underlined and contrasted with dissipative systems. Single-particle, rigid-body and collective motion problems are treated and simple harmonic motion is established as a fundamental mathematical model for physical systems. Galilean and Newtonian models of gravity are introduced and orbits and the Kepler problem are studied.

Entry Requirements

? Pre-requisites : Physics 1A (PHY-1-A); or SCE Advanced Higher or A-level Physics and Mathematics at A-grade; or SCE Higher Physics and Differential Equation Modelling & Solution (MAT-1-DMS). In addition Foundations of Calculus (MAT-2-FoC) and Several Variable Calculus (MAT-2-SVC) or suitable performance in AM3 (MAT-2-am3) and MM3 (MAT-2-mm3).

? Prohibited combinations : Foundations of Mathematical Physics (PHY-2-FoMP); AM4 (MAT-2-am4) and MM4 (MAT-2-mm4).

Subject Areas

Home subject area

Undergraduate (School of Physics and Astronomy), (School of Physics and Astronomy, Schedule Q)

Other subject areas

Specialist Mathematics & Statistics (Year 2), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 2nd year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 4 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
12/01/2009	11:00	12:00	Lecture Theatre C, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	11:10	12:00	KB
Lecture	Thursday	11:10	12:00	KB

? Additional Class Information : Workshops two hours per week, as arranged.

Summary of Intended Learning Outcomes

After completion of the course the student should demonstrate an ability to:

1. starting from Newton's second law as a differential equation, formulate one- and two-dimensional dynamical problems including motions under gravity, motions with resistive forces, motions with variable mass.

2. solve first and second order linear differential equations appearing in dynamical contexts; fit and interpret physical boundary and initial conditions.

3. define mathematically key physical quantities such as work, energy, momentum and angular momentum and derive conservation laws in relevant cases.

4. understand simple harmonic motion as a mathematical model including the roles of damping and forcing

5. understand motion in a general potential, classical limits of the motion and small oscillations near a potential minimum

6. understand the factorization of centre-of-mass and relative motion in many particle systems

7. model several-body systems by coupled differential equations, linearize near stable equilibria and derive normal mode solutions for collective motion

8. set up two and three dimensional dynamical problems in vector notation and simple non-Cartesian co-ordinate systems, in particular plane polar and spherical polar coordinates

9. set up and solve central force orbits; find solutions for circular motion and analyse their stability within a linear approximation

10. understand the meaning and the terms open, closed and stable orbits and the occurrence of elliptic, parabolic and hyperbolic orbits

11. understand motion in terms of scattering and scattering cross-sections in elementary cases

12. understand the importance of different frames of reference and transformations between them.