Advanced Mechanics I
PHYS 6412, Fall
2017
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, 13:0014:30
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 
Sep. 57 



2 
Principle of least action. Calculus
of variations 
L 12 
Sep. 1214 


G 1.3; 2.15 

3 
Lagrangian formalism 
L 35 
Sep. 1921 


G 1.46 

4 
Conservation laws 
L 610 
Sep. 2628 


G 2.67; 3.4 

5 
Integration of the equations of
motion in 1D 
L 1112 
Oct. 35 





EXAM 1 
Ch. L 13; G 13 
Oct. 19 
6 
Motion in a central field 
L 1314 
Oct. 1012 


G 3.13,56 

7 
Kepler’s problem 
L 15 
Oct. 1724 


G 3.79 

8 
Small oscillations in 1D 
L 2122,25 
Oct. 2631 


G 6.1,5 

9 
Principal axis of oscillations. Vibration of molecules 
L 2324 
Nov. 27 


G 6.24 


EXAM 2 
Ch. L 3,5; G 3,6 
Nov. 16 
10 
Rigid body motion 
L 3134 
Nov. 914 


G 4.13; 5.14 

11 
Euler angles. Euler's equations 
L 3536 
Nov. 2123 


G 4.4,6; 5.57 

12 
Hamiltonian formalism 
L 4041; 4344 
Nov. 2830 


G 8.1,3,56 

13 
Conservation laws. Poisson bracket 
L 42 
Dec. 5 


G 8.2; 9.5 

14 
Canonical transformations 
L 4546 
Dec. 712 


G 9.14, 7 


FINAL EXAM 
Ch. L 6,7; G 4,5,8,9 
Dec. 14 
G –
Goldstein; L – Landau & Lifshitz