• Analytical Mechanics
    • Department of Physics and Astronomy
    • Credit. 4
    • PH223
    • Enroll
    • WILL BEGIN
    • Fall , 2015
    • 981
    • Course Description:
    • The purpose of this course is to let students become familiar with some key concepts in analytical mechanics, including Newtonian mechanics, Lagrange's equations, Hamilton's principle, conservation theorems, two-body problems, the motion of rigid body, oscillation, canonical transformation, Poisson bracket, Hamilton-Jacobi theory. The class is taught along two lines: one with the explanations of real-life examples and the corresponding problem-solving techniques; the other with the introduction of the history of mechanics and its relation with modern developments of physics, including quantum mechanics and relativity.
    • Course Syllabus:
    • I. Newtonian Mechanics:
      The concept of point mass particle, position, velocity, linear momentum, angular momentum, Newton's laws, conservation laws, inertial frame, non-inertial frame (the Coriolis effect), conservative forces, mechanics of multiple particles;

      II. Variational Principles and Lagrange's Equations:
      Constraints, D'Alembert's principle,
      Lagrange's equations, applications of Lagrangian formulation,
      Hamilton's principle, conservation theorems and symmetry properties;

      III. The Central Force Problem:
      Equations of motion, integrals of motion, the differential equation for the orbit, Kepler problem, harmonic oscillator, scattering problem, transition from the lab frame to center-of-mass frame;

      IV. The Kinematics of Rigid Body Motion:
      The independent Coordinates of a Rigid Body, Euler angles, finite rotations, infinitesimal rotations, angular momentum and kinetic energy of motion about a point, the inertia tensor and the moment of inertia, eigenvalues of the inertia tensor and the principle axis, Euler equations of motion, torque-free motion of a rigid body;

      V. Oscillations:
      The eigenvalue equation, normal coordinates;

      VI. The Hamilton Equations of Motion:
      Hamilton equations of motion, cyclic coordinates and conservation theorems, the principle of least action;

      VII. Canonical Transformations:
      Four types of canonical transformation, direct conditions for canonical transformation, Poisson Brackets/canonical invariants, equations of motion, infinitesimal canonical transformations, and conservation theorems in the form of Poisson Bracket, angular momentum Poisson Bracket relations, Liouville's theorem;

      VIII. Hamilton-Jacobi Theory:
      The Hamilton-Jacobi Equation, the canonical perturbation theory.
    • Schedule:
    • Class Meeting Time: 1st-16th week, twice per week, 90minutes per class;
      Class Meeting Place: on campus;
      Mid-term exam time: middle of the semester;
      Final exam time: after the 16th week;
      Grading Criteria: 20% Homework,10% Thesis, 20% Midterm Exam, 50%
  • Reading list
  • Other Materials
  • Discussion
  • Homework download/submit
    • 张骏
    • Associate Professor
    • Read more
    • Male
    • E-mail:
    • betajzhang@sjtu.edu.cn
    • Profile
    • I grew up in Shanghai, China. I got my B.S. in Physics from Fudan University in 2000, and Ph.D. in Physics from Columbia University in 2006. I was a TAC postdoctoral fellow in UC Berkeley from 2006 to 2009, and a TCC postdoctoral fellow of Texas Cosmology Center (UT Austin) from 2009 to 2012. I joined the faculty of Shanghai Jiao Tong University in 2012.

      I am interested in the formation of the large scale structure in our Universe, and the underlying physical rules. Theoretically, my research focuses on understanding the properties of dark matter, dark energy, cosmic microwave background, galaxies, clusters, cosmic reionization, etc.. Observationally, we use the gravitational lensing effect to directly probe the density distribution of our Universe, and to test the theory of gravity on the cosmic scales.
  • Prerequisite Course:

    Mechanics

  • Textbooks:

    Classical Mechanics, By Herbert Goldstein & Charles Poole
  • Grading:

    Homework: 20%;
    Mid-term exam: 30%
    Final exam: 40%
    Thesis: 10%
Other courses
  • Thermodynamics and Statistical Physics
    Thermodynamics and Statisti...
    Physics 303 is an advanced undergraduate course in thermodynamics and statistical physics. Thermodynamics covers the macroscopic properties of physical systems, composed of large numbers of particles....
    王顺
    1159
  • Biophysics
    Biophysics
    This course gives a complete overview of physical phenomena of biological systems, with an emphasis on computational biophysics, molecular modeling, and the simulation of biophysical systems.
    Jakob Ulmschneider
    846
  • Classical Electrodynamics
    Classical Electrodynamics
    This is a fundamental course for undergraduate students of department of physics. It includes electrostatics, magnetostatics, Maxwell Equations, electromagnetic waves and radiation, and fundamental pr...
    陈民
    1473
  • Analytical Mechanics
    Analytical Mechanics
    The purpose of this course is to let students become familiar with some key concepts in analytical mechanics, including Newtonian mechanics, Lagrange's equations, Hamilton's principle, conservation th...
    张骏
    981
  • Intermediate Theoretical Methods
    Intermediate Theoretical Me...
    Intermediate Theoretical Methods is a basic course required for undergraduate students in the Department of Physics and Astronomy at Shanghai Jiao Tong University. The course covers several topics, in...
    罗卫东
    749
  • Plasma Physics
    Plasma Physics
    The course is introductory-level plasma physics where I teach students the fundamental concepts, theories and some potential applications for plasma physics. Fundamental theories include single-partic...
    Nasr Hafz
    943
  • Experimental Physics III
    Experimental Physics III
    This is an experimental course to provide junior students to conduct experiments in a laboratory environment. The topics include mechanics, optics, electromagnetism, and atomic physics. Some experimen...
    倪凯旋
    689
  • Introduction of physics Research II
    Introduction of physics Res...
    This course is the second part of the “Introduction to Physics Research”. The idea of the course is to give a brief introduction to the freshmen about the meaning of physics research nowadays. The cou...
    刘灿华
    929
  • 物理学引论(A类)(2)
    物理学引论(A类)(2)
    This course will cover topics in two major areas: (1) thermal and stastical physics; (2) Waves and vibrations.
    张洁
    574

Shanghai Jiao Tong University The English Course Catalog | School Counseling:021-34206468-102

沪ICP备05052060 © Shanghai Jiao Tong University all rights reserved. | Address: 800 Dongchuan Road, Shanghai