OUTLINE 大纲

物理竞赛

PART I MECHANICS 经典力学

I.1 Kinematics 运动学

I.1-1 Linear Motion 直线运动

- Speed, Velocity, Acceleration
- Differential, Integral

I.1-2 2-D and 3-D Trajectories 平面与空间轨迹

- Vectors, Projectile Trajectories
- Circular Motion, Normal Acceleration, Tangential Acceleration
- Polar Coordinates, Radical Acceleration, Angular Acceleration
- Arbitrary 2-D Motions, Radii of Curvature, Some Simple 3-D Motions

I.1-3 Relative Kinematics 相对运动

- Translational Reference Frame, Relative Velocity, Relative Acceleration
- Rotational Reference Frame, Relative Velocity in Rotational Frame, Relative Acceleration in Rotational Frame

I.1-4 Kinematics of a Rigid Body 刚体运动

- Degree of Freedom, Translation, Simple Rotation
- Plane-parallel Motion, Precession and Mutation

I.2 Statics 静力学

I.2-1 Equilibrium of a Point Mass 质点的平衡

- Force, Simplification of Force Systems
- Equilibrium of Forces, Multi Objects

I.2-2 Equilibrium of a Rigid Body 刚体的平衡

- Moment of Force, Torque, Equilibrium of Torque
- Equilibrium of Arbitrary Object, Centre of Mass

I.2-3 Stability of Equilibrium 平衡的稳定性

- Stable Equilibrium, Unstable Equilibrium, Neutral Equilibrium
- Stability, Potential function

I.3 Dynamics 动力学

I.3-1 Newton's First and Third Law of Motion 牛顿的第一和第三定律

- Newton's First Law, Inertia, Inertial Frame and Relativity
- Newton's Third Law, Internal Force and External Force

I.3-2 Newton's Second Law of Motion 牛顿的第二定律

- Newton's Second Law of Motion, Differential Equations
- Non-inertial Frame, Pseudo Force

I.3-3 Momentum 动量

- Momentum, Centre of Mass Motion
- Impact, Transfer of Momentum
- Dynamics of a Variable Mass, Rocket Dynamics

I.3-4 Energy 能量

- Work, Energy, Kinetic Energy, Conservative Force and Potential
- Work-Energy Theorem, Two-Body Systems

I.3-5 Conservation Laws 守恒律

- Conservation of Momentum, Conservation of Energy
- Collisions, Cross-Sections, Particle Experiments

I.4 Topic A: Central Force 中心力

I.4-1 Angular Momentum 角动量

- Rotation in Central Force Fields, Angular Momentum, Conservation of Angular Momentum
- Moment of Impact, Angular Momentum Theorem

I.4-2 Central Force Field 中心力场

- Potential, Equation of Motion, Effective Potential
- Harmonic Field
- Gravitational Field, Kelper's Law, Conservatives in Gravitational Fields
- Orbits, LRL Vector, Orbital Transfer Problems
- Celestial Two-Body Problems

I.5 Topic B: Rigid Body 刚体

I.5-1 Rotation of a Rigid Body 刚体的转动

- Angular displacement, Angular Velocity
- Angular Momentum Theorem for a Rotating Rigid Body, Moment of Inertia, Angular Acceleration

I.5-2 General Motion of a Rigid Body 刚体的一般运动

- Plane-parallel Motion, Precession and Mutation Formula
- Vector of Angular Velocity, Tensor of Interial, Euler's Equation

I.6 Topic C: Vibrations and Waves 振动与波动

I.6-1 Simple Harmony 简谐运动

- Equation of Motion, Second Order ODE Theory, Complex Numbers
- Phase, Frequency, Amplitude and Period
- Velocity and Acceleration, Energy in Simple Harmony
- Other Forms of Simple Harmony, Criterions, Tylor Expansion
- Damped Oscillator, Forced Vibration, Resonance

I.6-2 Synthesis of Simple Harmonies 简谐运动的合成

- Synthesis of Simple Harmonies with the Same Frequency in the Same Direction, Case of various Frequencies
- Synthesis of Simple Harmonies in two Directions, Lissajous Figure

I.6-3 Waves 波

- Wave Equation, WaveLength, Wave Vector, Phase Velocity
- Energy in Wave, Energy Flux in Wave
- Reflection, refraction, interference and Diffraction
- Standing Wave, Group Velocity, Dispersion of Waves

PART II ELECTROMAGNETISM

II.1 Electrostatics
II.2 Circuits
II.3 Magnetostatics
II.4 Electromagnetic Induction
II.5 Electromagnetism in Medias
II.6 Maxwell's Theory

PART III THERMOLOGY

III.1 Temperature and States
III.2 First Law of Thermodynamics
III.3 Second Law of Thermodynamics
III.4 Statistical View of Thermology

PART IV OPTICS

IV.1 Geometrical Optics
IV.2 Wave Optics

PART V MODERN PHYSICS

V.1 Optoelectronic Effect and Light Quanta
V.2 Quantisation of Atom Dynamics
V.3 Introduction to Quantum Mechanics
V.4 Special Relativity
V.5 Introduction to General Relativity