• Analytical Mechanics
    • Department of Physics and Astronomy
    • Credit. 4
    • PH223
    • Enroll
    • 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:


  • Textbooks:

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

    Homework: 20%;
    Mid-term exam: 30%
    Final exam: 40%
    Thesis: 10%
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