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DRPS : Course Catalogue : School of Physics and Astronomy : Undergraduate (School of Physics and Astronomy)

Undergraduate Course: Lagrangian Dynamics (PHYS10015)

Course Outline
SchoolSchool of Physics and Astronomy CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) Credits10
Home subject areaUndergraduate (School of Physics and Astronomy) Other subject areaNone
Course website None Taught in Gaelic?No
Course descriptionThe principles of classical dynamics, in the Newtonian formulation, are expressed in terms of (vectorial) equations of motion. These principles are recapitulated and extended to cover systems of many particles. The laws of dynamics are then reformulated in the Lagrangian framework, in which a scalar quantity (the Lagrangian) takes centre stage. The equations of motion then follow by differentiation, and can be obtained directly in terms of whatever generalised coordinates suit the problem at hand. These ideas are encapsulated in Hamilton's principle, a statement that the motion of any classical system is such as to extremise the value of a certain integral. The laws of mechanics are then obtained by a method known as the calculus of variations. As a problem-solving tool, the Lagrangian approach is especially useful in dealing with constrained systems, including (for example) rotating rigid bodies, and one aim of the course is to gain proficiency in such methods. At the same time, we examine the conceptual content of the theory, which reveals the deep connection between symmetries and conservation laws in physics. Hamilton's formulation of classical dynamics (Hamiltonian Dynamics) is introduced, and some of its consequences and applications are explored.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Other requirements Students should have achieved the learning outcomes of Dynamics (PHYS08040), together with knowledge of basic algebra and calculus corresponding to material in Mathematics for Physics 1 (PHYS08035), linear algebra and multivariate calculus corresponding to the material in Algebra and Calculus (PHYS08041), or their equivalents.
Additional Costs None
Information for Visiting Students
Displayed in Visiting Students Prospectus?Yes
Course Delivery Information
Delivery period: 2014/15 Semester 1, Available to all students (SV1) Learn enabled:  Yes Quota:  None
Web Timetable Web Timetable
Class Delivery Information Workshop/tutorial sessions, as arranged.
Course Start Date 15/09/2014
Breakdown of Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 20, Summative Assessment Hours 2, Revision Session Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 52 )
Additional Notes
Breakdown of Assessment Methods (Further Info) Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)2:00
Summary of Intended Learning Outcomes
Consolidation of the learning outcomes in the Entry Requirements in the context of more challenging classical dynamics problems, together with at least two of the following:

a. understanding of the Lagrangian formulation of classical dynamics and the ability to apply it to solve for the motion of point particles and simple bodies in terms of generalised coordinates;

b. understanding of the relationship between symmetries and conservation laws, and knowledge of the Hamiltonian formulation of classical dynamics and Poisson brackets;

c. ability to apply the calculus of variations to solve minimisation problems, and knowledge of the formulation of dynamics in terms of a variational principle;

d. ability to apply Lagrangian methods to solve for the motion of rigid bodies;

e. ability to solve for the small amplitude oscillations of coupled systems.
Assessment Information
Degree Examination, 100%
Special Arrangements
Additional Information
Academic description Not entered
Syllabus - Revision of Newtonian Mechanics: Newton's laws; Dynamics of a Particle; Conservation Laws
- Dynamics of a system of particles; Momentum; Angular Momentum; Energy; Transformation Laws
- Use of centre of momentum; Noninertial rotating frames; Summary of Newton's scheme
- Constraints; Generalised coordinates and velocities
- Generalised forces; Derivation of the Lagrange equation
- Lagrangian; Examples
- Using Lagrangian Method. Examples: Atwood's Monkey; particle and wedge; simple pendulum; spherical pendulum
- Rotating frames; Calculus of Variations
- Applications of Variational Calculus; Hamilton's Principle
- Hamilton's Principle; Conservation Laws; Energy Function
- Energy Function; Conservation Laws and Symmetry
- Velocity-dependent Forces;
- Hamiltonian Dynamics; relationship to Quantum Mechanics
- Rigid Body Motion; Introduction; Euler's Equations
- The Symmetric Top - Precession; the Tennis Racquet Theorem
- Lagrangian for a Top; Equations of motion; Conservation Laws
- Symmetric Tops: Zones; Steady Precession; Nutation; Gyroscopes
- Small Oscillation Theory
Transferable skills Not entered
Reading list Not entered
Study Abroad Not entered
Study Pattern Not entered
Course organiserProf R Kenway
Tel: (0131 6)50 5245
Course secretaryMrs Bonnie Macmillan
Tel: (0131 6)50 5905
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