Syllabus for Theoretical Mechanics
PHYS3108
Current Lecturer
Prof. Zhouzhou SUN Email: phzzsun@suda.edu.cn
Course Time
4th Semester
Lectures: 3 sessions/week, 50min /session. 18 weeks.
Course Description
Theoretical Mechanics is an advanced course to mechanics in macro world. Using calculus tools, including solving ordinary differential equations, classical mechanics teaches the students the general theories of Newtonian mechanics and analytical mechanics. The topics include: Newtonian mechanics of one particle and particles, Analytical mechanics including Lagrange form and Hamilton’s form, Central force problem, Non-inertial rotational reference system, Rigid body motion and Oscillating systems, etc.
Prerequisites
General Physics I (PHYS1025); Method of Mathematical Physics (PHYS3103)
Textbooks
Analytical Mechanics (7ed), by G.R. Fowles and G.L. Cassiday, (Brooks/Cole, 2005).
Lectures on Classic Mechanics, by X.F. Zhong, (CUST, 2011)；钟学富，《经典力学讲义》，（中科大出版社，2011）.
Reference books
周衍柏，《理论力学教程》（第三版），（高教社，2009）。
Classical Mechanics (3rd), by H. Goldstein, et al., (高教社，2005).
Mechanics, by L.D. Landau and E.M. Lifshitz, (世界图书出版公司，1999).
Main contents
Week | Teaching Contents | Sessions | Objectives |
1 | Introduction; Mathematics preparation (I) | 3 | vectors, vector products |
2 | Mathematics preparation (II) | 3 | coordinates system; velocity, acceleration, orbit |
3 | Newtonian mechanics of one particle | 3 | Newton's equations, exercise |
4 | Position, velocity-dependent force | 3 | kinetic and potential energy, exercise |
5 | Analytical mechanics; Generalized coordinate, velocity | 3 | concepts in analytical mechanics: constrains, generalized coordinate |
6 | Lagrange's equations | 3 | derivation of Lagrange's equations, exercise |
7 | Hamilton's equations | 3 | derivation of Hamilton's equations, exercise |
8 | Gravitation, central force problem | 3 | central force problem, exercise |
9 | Non-inertial reference system, rotating coordinate system | 3 | non-inertial reference system, inertial force, rotating coordinate system |
10 | Midterm Exam | 3 | midterm exam |
11 | Mechanics of particles; Conservation laws | 3 | particles mechanics; momentum, angular momentum, energy |
12 | Two-body problem, center of mass | 3 | two-body problem, center of mass motion, exercise |
13 | Rigid body; Angular velocity | 3 | concepts of rigid body, angular velocity |
14 | Euler angles; Moment of inertia | 3 | Euler angles, moment of inertia |
15 | Rotation around fixed axes; Planar motion | 3 | rotation around fixed axes, planar motion, exercise |
16 | Rotation around fixed point | 3 | rotation around fixed point, Euler equations, exercise |
17 | Oscillating systems | 3 | multiple atoms oscillations, normal coordinates |
18 | Review, Exercise | 3 | general review for final exam |
Marking Scheme:
Attendance | Homework & Quiz | Midterm | Final exam |
10% | 20% | 30% | 40% |
