### Theoretical Mechanics

Course Code: B22001Y-01

Course Name: Theoretical Mechanics

Credits: 4.0

Lecture Time: 36 sessions, 2 hours/session

Course Description

As the first major compulsory physical course for undergraduate students majoring in Physics, this course is designed to help students systematically master basic content of Newtonian Mechanics, Lagrangian mechanics, and Hamiltonian mechanics and understand the relationship and equivalence between them. We also aim at reinforcing students to fully understand classical mechanics and improving students' ability of abstract thinking in Physics. We hope students will obtain a preliminary understanding of the principles of symmetry, method of taking limit and some approximation methods of solving physical problems such as small quantity expansion. Students' ability to solve practical physical problems with the theoretical mechanics knowledge should be improved.

Topics and Schedule

1. Introduction (4 hrs)

1.1. A brief history of the development of classical mechanics (1.5 hrs)
1.2. The relation between analytic mechanics and vector mechanics (2 hrs)
1.3. Some illustration about text book, teaching and examination (0.5 hrs)

2.  Classical Mechanics Foundation (10 hrs)
2.1 Newton mass point and mechanics of mass point system
2.1.1 Description method of motion (0.5 hrs)
2.1.2 Translation and rotation reference frame (0.5 hrs)
2.1.3 Newton particle dynamics  (1 hrs)
2.1.4 Conservation law in particle mechanics (1 hrs)
2.1.5 Particle system dynamics (1 hrs)
2.2 Newton-Euler rigid body mechanics
2.2.1 Basic motion of rigid body (1 hrs)
2.2.2 Simple motion of rigid body (1 hrs)
2.2.3 Kinematic parameters of fixed point motion of rigid body and Euler  kinematic equation (1 hrs)
2.2.4 Angular momentum and rotational kinetic energy of rigid body fixed point motion (1 hrs)
2.2.5 Euler kinetic equation and its exact solution (1 hrs)
2.2.6 Tensor representation of inertia tensor and rigid body mechanics (1 hrs)

3.  Lagrangian Mechanics (20 hrs)
3.1 Basic concepts and basic principles of analytical mechanics

3.1.1 Basic concepts of analytical mechanics (2 hrs)

3.1.2 Variation method (2 hrs)

3.1.3 Hamilton principle (2 hrs)
3.2 Lagrange equation
3.2.1 Lagrange equation (2 hrs)
3.2.2 The solution of Lagrange equation (2 hrs)
3.2.3 Principle of virtual work (principle of virtual displacement) (2 hrs)
3.2.4 Research of Lagrange equation (2 hrs)

3.3 Simple integrable system

3.3.1 Integrable systems and non-integrable systems (1 hrs)
3.3.2 Mechanical system of single freedom degree freedom (1 hrs)
3.3.3 Micro vibration of multi freedom degree mechanical system (1 hrs)
3.3.4 Normal coordinates, normal frequency and normal vibration (1 hrs)
3.3.5 Application example of micro vibration theory (1 hrs)
3.3.6 Kepler problem (1 hrs)

4.  Hamiltonian Mechanics (20 hrs)
4.1 Hamiltonian canonical equation
4.1.1 Hamiltonian canonical equation (2 hrs)
4.1.2 Solutions and integrals of Hamiltonian canonical equations (2 hrs)
4.1.3 Examples of application of Hamiltonian canonical equations (2 hrs)
4.1.4 Research of Hamiltonian canonical equations (1 hrs)
4.2 Canonical transformation
4.2.1 Canonical transformation (2 hrs)
4.2.2 The condition of canonical transformation (1 hrs)
4.2.3 Infinitesimal canonical transformation (1 hrs)
4.2.4 Hamilton-Jacobi equation (3 class hours)
4.2.5 action variables and angular variables (2 hrs)
4.2.6 Poisson bracket (2 hrs)
4.3 Liouville theorem (2 hrs)
Lecture time: 54 hrs

Exercise class: 14 hrs

Midterm examination: 2 hrs

Final examination: 2 hrs

Closed-book written examination
Daily assignments 10
, Midterm examination 40, Final examination 50

Textbook

Hui-Chuan Shen, Shu-Min Li, Classical Mechanics, University of Science & Technology of China Press

References
[1] Yan-Bai Zhou, a Course in Theoretical Mechanics (Recommended Reference);
[2] (Russia)Л.Д .Landau
(Russia) Е.М. Lifshitz,
a Course in Theoretical Physics, Vol. 1, Mechanics, Higher Education Press. (Recommended Reference);
[3] Hui-Chuan Shen
Li Shen, Problem Spectrum of Classical Mechanics, Classical Mechanics, University of Science & Technology of China Press (Teachers' reference book).