Advanced Mechanics I
PHYS 6412, Fall 2018
Instructor:
Prof. Julian Velev
Office:
Natural Sciences II, C346
Email: julian.velev@upr.edu
Class
period: Tuesday and Thursday, 11:3012:50,
room C311
Office
hours: Tuesday and Thursday, 13:0014:00
or by appointment
Course description: This course will reiterate
the subject of classical mechanics familiar to the student from undergraduate
courses. However, this will be done on firm ideological and mathematical
grounds. This will give the student the opportunity to learn a
number of important mathematical techniques which are used in other
branches of physics and in other fields. In addition, the advanced formulation
of classical mechanics is a stepping stone to various other branches of modern
physics such as quantum mechanics, statistical mechanics, etc. The course will cover
the Lagrangian and Hamiltonian formulation of mechanics; conservation laws; and
integration of the equations of motion for the one and two body problems.
Important special cases will be covered in detail, such as motion in a central
field; motion of a rigid body; and small oscillations.
Prerequisites: The students should be familiar with the Newtonian
formulation of mechanics (undergraduate courses) and should have sufficient mathematical proficiency.
Textbooks: (1) L.D. Landau and E.M. Lifshitz,
Mechanics (Vol. 1, Third Edition), Elsevier, ISBN 0750628960; (2)
H. Goldstein, Classical Mechanics
(3rd Edition), AddisonWesley, ISBN 0201657023
Grading: There will be three exams, each exam counts for 30% of the
grade. The exams will be in class and noncumulative. The remaining 10% of the
grade will be for class attendance and participation, and for doing reading and
homework assignments.
Special provisions: (1) Missed classes: if a
class is lost due to travel or other circumstances I will assign times when the
class will be madeup and/or assign equivalent reading and homework
assignments; (2) Special arrangements: homework extensions, makeup exams, and
other exceptions can be granted given sufficient
reason and advanced notice.
Academic integrity: The University of Puerto
Rico promotes the highest standards of academic and scientific integrity. Article
6.2 of the UPR Students General Bylaws (Board of Trustees Certification 13,
20092010) states that academic dishonesty includes, but is not limited to:
fraudulent actions; obtaining grades or academic degrees by false or fraudulent
simulations; copying the whole or part of the academic work of another person;
plagiarizing totally or partially the work of another person; copying all or
part of another person answers to the questions of an oral or written exam by
taking or getting someone else to take the exam on his/her behalf; as well as
enabling and facilitating another person to perform the aforementioned behavior.
Any of these behaviors will be subject to disciplinary action in accordance
with the disciplinary procedure laid down in the UPR Students General Bylaws.
Tentative
class schedule:
Week 
Topics 
Reading 
Dates 
1 
Survey of Newtonian mechanics 
G 1.12 
Aug. 2123 



2 
Principle of least action. Calculus
of variations 
L 12 
Aug. 2830 


G 1.3; 2.15 

3 
Lagrangian formalism 
L 35 
Sep. 46 


G 1.46 

4 
Conservation laws 
L 610 
Sep. 1113 


G 2.67; 3.4 

5 
Integration of the equations of
motion in 1D 
L 1112 
Sep. 1820 





EXAM 1 
Ch. L 13; G 13 
Oct. 2 
6 
Motion in a central field 
L 1314 
Sep. 2527 


G 3.13,56 

7 
Kepler’s problem 
L 15 
Oct. 49 


G 3.79 

8 
Small oscillations in 1D 
L 2122,25 
Oct. 1116 


G 6.1,5 

9 
Principal axis of oscillations. Vibration of molecules 
L 2324 
Oct. 1823 


G 6.24 


EXAM 2 
Ch. L 3,5; G 3,6 
Nov. 1 
10 
Rigid body motion 
L 3134 
Oct. 2530 


G 4.13; 5.14 

11 
Euler angles. Euler's equations 
L 3536 
Nov. 68 


G 4.4,6; 5.57 

12 
Hamiltonian formalism 
L 4041; 4344 
Nov. 1315 


G 8.1,3,56 

13 
Conservation laws. Poisson bracket 
L 42 
Nov. 2027 


G 8.2; 9.5 

14 
Canonical transformations 
L 4546 
Nov. 29Dec. 4 


G 9.14, 7 


FINAL EXAM 
Ch. L 6,7; G 4,5,8,9 
Dec. 6 
G –
Goldstein; L – Landau & Lifshitz