Undergraduate Course: Lagrangian Dynamics (PHYS10015)
Course Outline
School  School of Physics and Astronomy 
College  College of Science and Engineering 
Course type  Standard 
Availability  Available to all students 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Credits  10 
Home subject area  Undergraduate (School of Physics and Astronomy) 
Other subject area  None 
Course website 
None 
Taught in Gaelic?  No 
Course description  The 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 problemsolving 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)
Prerequisites 

Corequisites  
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
Prerequisites  None 
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
None 
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
 Velocitydependent 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 
Keywords  LagD 
Contacts
Course organiser  Prof R Kenway
Tel: (0131 6)50 5245
Email: R.D.Kenway@ed.ac.uk 
Course secretary  Mrs Bonnie Macmillan
Tel: (0131 6)50 5905
Email: Bonnie.MacMillan@ed.ac.uk 

