古典力學（一）

Goals: This course offers an advanced (mathematical) formulation of classical mechanics, served as a springboard for various branches of modern quantum physics. General description: Foundations of mechanics are formulated via variational principle and Lagrangian formulism, canonical transformations , Poisson bracket formulation, Hamilton-Jocobi theory, and action-angle variables. Mathematical techniques are used to broaden various kinds of mechanical problems and to make contact to quantum mechanics, such as: scattering theory in central force motions, eigenvalue problem of orthogonal matrix for rigid body rotation, field theory for continuous systems.

Prerequisite: General Physics, Mechanics (undergraduate level), Calculus, Applied Math (Mathematical Physics)

無備註

Teaching approaches/methodology: This course is given in English. Blackboard lectures. There will be a Teaching Assistant (TA), who helps to grade homework, exam. The solutions of homework and important notices/announcements/lecture notes will be announced via NCTU e3-platform through NCTU’s website.

Homework, Exams, Grading policy Weekly homework, 70% No midterm exam Final take-home exam 30%

• Variational Principles and Lagrange’s Equations

  1. Hamilton’s principle 2. Calculus of variations 3. Derivation of Lagrange’s equations from Hamilton’s principle 4. Conservation theorems

  講授：

  6

• The central force problem

  1. Equations of motion and first integral 2. The equivalent 1-dimensional problem 3. The Virial theorem 4. The differential equations for the orbit 5. Condition for closed orbit 6. The Kepler problem 7. Scattering in a central force field

  講授：

  6

• The kinematics of rigid body motion

  1. Orthogonal coordinate transformation and transformation matrix 2. The Euler’s angles and Euler’s theorem on the rigid body motion 3. Infinitesimal and finite rotations 4. The Coriolis effect

  講授：

  4

• The rigid body equation of motion

  1. Angular moment and kinetic energy 2. The inertial tensor and the moment of inertial 3. The eigenvalues of inertial tensor and principal axis transformation 4. Rigid body problem and Euler’s equations of motion 5. Torque-free rigid body 6. Motion of a symmetrical top

  講授：

  5

• Oscillations

  1. The eigenvalue equation and the principal axis transformation 2. Free vibrations and normal coordinates 3. Forced vibrations 4. The damped driven pendulum

  講授：

  3

• The Hamilton equations of motion

  1. Legendre transformation 2. Cyclic coordinates and conservation theorem 3. The Routh’s procedure 4. Derivation of Hamilton principle from variational principle 5. The principle of least action

  講授：

  5

• Canonical transformations

  1. The equations of canonical transformation 2. Examples of canonical transformation 3. Harmonic oscillator 4. The symplectic approach 5. Poisson bracket 6. Equations of motion, infinitesimal canonical transformations, and conservation theorem in Poisson bracket formulation 7. The angular momentum Poisson bracket relations 8. The Liouville’s theorem

  講授：

  7

• Hamilton-Jacobi theory and Action-Angle variables

  1. The Hamilton-Jacobi equation 2. Harmonic oscillator problem via Hamilton-Jacobi approach 3. Hamilton’s characteristic function 4. Separation of variables 5. The Keppler’s problem revisit via action-angle variable

  講授：

  5

• Canonical perturbation theory

  1. Time-dependent perturbation 2. Time-independent perturbation theory

  講授：

  3

• Lagrangian and Hamiltonian formulations for continuous systems and fields

  1. From discrete to continuous system 2. Lagrangian formulation for continuous systems 3. Stress energy tensor and conservation theorems 4. Hamiltonian formulation 5. Neother’s theorem

  講授：

  6

• Elementary Principles of Mechanics

  1. . review of Newtonian mechanics 2. D’alembert’s principle and Lagrange’s equations

  講授：

  2

Classical Mechanics, by Herbert Goldstein, Pearson Education Limited, 2014 (3rd Edition)

地點

SC452

時間

Wed. 1:30-2:30pm

聯絡方式

Tel: ext. 56107 chung@mail.nctu.edu.tw