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課程概述 |
基礎的質點及質點系古典力學。
課程綱要如下，章節編號基於指定閱讀( Thorton and Marion 第五版)：
1. Newtonian mechanics — Single particle (Ch.2)
1.1 The state of motion and the ideation of force (S.2.1)
1.2 The three laws of motion of Newton (S.2.2)
1.3 Frames of reference (S.2.3)
1.4 The equation of motion (EOM) of a particle (S.2.4)
1.5 Conserved quantities according to Newton’s laws (S.2.5)
1.6 Energy (S.2.6)
1.7 Beyond Newtonian mechanics — Relativity and quantum physics (S.2.7)
2. Brief introduction to Lagrangian and Hamiltonian dynamics (Ch.6 and 7)
2.1 Euler equations (S.6.1 ~ 5)
2.2 Constraints and generalized coordinates (S.6.6 and 7, S.7.1 ~ 3)
2.3 Lagrange’s equations (S.7.4 ~ 9)
2.4 Canonical equation of motion, Hamiltonian mechanics, and energetic point of view (S.7.10 ~ 13)
3. Classical gravitation, central force, and celestial applications (Ch.5 and 8)
3.1 Gravitational field and potential (S.5.1 ~ 3)
3.2 Usefulness of potential concept (S.5.4)
3.3 Two-body center-of-mass coordinates and reduced mass (S.8.1 - 2)
3.4 First integrals and conservation theorems in two-body systems (S.8.3)
3.5 Equations of motion (S.8.4)
3.6 Kinematics and energetics of orbits in a central field (S.8.5 - 7)
3.7 Dynamics and stability of orbits in a central field (S.8.8 - 10)
4. Dynamics of a system of particles (Ch.9)
4.1 Center of mass (S.9.1 ~ 2)
4.2 Linear momentum (S.9.3)
4.3 Angular momentum (S.9.4)
4.4 Energy of a system (S.9.5)
4.5 Collisions, elastic and inelastic (S.9.6 ~ 8)
4.6 Probability: Scattering (S.9.9 ~ 10)
4.7 Continuous case: Rocket motion (S.9.11)
5. Noninertial reference frame (Ch.10)
5.1 Rotating coordinate systems (S.10.1 ~ 2)
5.2 Centrifugal and coriolis forces (S.10.3)
5.3 Motion relative to the Earth (S.10.4)
6. Rigid bodies (Ch.11)
6.1 Planar motion and angular momentum (S.11.2 and 4)
6.2 Principal axes of inertia and different body coordinate systems (S.11.5 ~ 7)
6.3 Eulerian angles and Euler equations (S.11.8 ~ 9)
6.4 Symmetric tops (S.11.10 ~ 11)
6.5 Stability of rigid-body rotation (S.11.12)
7. Coupled oscillations (Ch.12)
7.1 Two coupled harmonic oscillators and the weak-coupling limit (S.12.1 ~ 3)
7.2 General problem of coupled oscillations (S.12.4)
7.3 Eigen-modes, normal coordinates, and molecular vibrations (S.12.5 ~ 7)
7.4 Degeneracy: three linearly-coupled plane pendula (S.12.8)
7.5 Continuous case: the loaded string
8. Special theory of relativity (Ch.13)
8.1 Lorentz transformation (S.13.3)
8.2 Relativistic Doppler effect (S.13.5)
8.3 Relativistic momentum and energy (S.13.7 ~ 8)
8.4 Lagrangian function in special relativity (S.13.10)
8.5 Relativistic kinematics (S.13.11) |