Mechanics

As an introduction to physics, some typical examples and mathematical tools will be presented.
Here is assumed that the reader has knowledge of high school physics and mathematics.

Basics of Mechanics

Introduction

  1. Degree of Freedom
  2. Coordinate
  3. Position Vector
  4. Scalar and Vector triple product
  5. Speed
  6. Limit
  7. Differentiation
  8. Velocity
  9. Differentiation and Limit
  10. Integration
  11. Definite Integration
  12. Acceleration
  13. Taylor’s Theorem
  14. Calculus of multivariable functions

Law of Motion

Introduction

  1. Laws of motion
  2. Galilean principle of relativity
  3. Uniform Gravity
  4. Friction force
  5. Air resistance
  6. Constant velocity circular motion
  7. Non-inertial frame
  8. Symmetry
  9. Law of energy conservation
  10. Line Integral
  11. Principle of Energy and Conservative Force
  12. Law of Momentum Conservation
  13. Single Pendulum
  14. Two-body problem
  15. Elastic Collision
  16. Impulsive Force
  17. Unit and Dimension

Theory of Oscillation

Introduction

  1. Simple Oscillation
  2. Decay Oscillation
  3. Two-body problem of Oscillation
  4. Matrix
  5. Determinant
  6. Eigenvalue Problem for Real Symmetric Matrices
  7. Modes of Oscillation; Two-body
  8. Modes of Oscillation; Many-body
  9. Modes of Oscillation; Periodic Boundary Condition
  10. Forced Oscillation
  11. Resonance

Central Force

  1. Solving for the Central Force
  2. Polar Coordinate
  3. Central Force and Polar Coordinate
  4. Coulomb Potential
  5. Newtonian Gravity and Field
  6. Kepler’s Laws
  7. Laplace–Runge–Lenz Vector
  8. Volume Integral
  9. Solid Angle
  10. Theory of Scattering
  11. Scattering Problem; Rigid-body Sphere Potential
  12. Scattering Problem; Coulomb Potential

Mechanics of Rigid-body

  1. Equation of Motion in Non-inertial System
  2. Coriolis Force on Earth
  3. Equation of Motion of Rigid-body
  4. Calculation of Momentum of Inertia
  5. Rotational Motion around an Arbitrary Point
  6. Mechanical Equilibrium of Rigid-body
  7. Rigid-body Pendulum
  8. Principal Axes of Inertia
  9. Euler Angles
  10. Free Motion of Rigid-body
  11. Motion of Cylinder
  12. Motion of Rigid-body with Impulsive Force
  13. Motion of Symmetric Top
  14. Gyro Effect
  15. Newtonian Gravity of Rigid-body
  16. Tidal Force