Classical Mechanics - Introduction

Posted on Edited on In

This is the summary for myself to review the essential concepts that I learned in classical mechanics. There should be some wrong information that I might fix. I wish the whole process can be finished in a year for writing this note. This should be useful for reviewing the classical mechanics.

Introduction

The fundamental concept of establishing physics

Based on the macroscopic picture of the world, physics is a subject that try to find the general law for understanding the world. Therefore, the basic understanding is the motion of an object, which is the position and the time. For a single point particle in an isolated system without any external interaction, with the initial velocity and the position, the status of the system can be well defined.

  • Law
    Induction from the most fundamental observation concludes with simple rules, which can only applied in specific condition and with some exceptions.

  • Principle
    The rule widely accepted nearly without any exceptions.

  • Theory
    The concrete theoretical system to explain the whole phenomena in a reasonable

  • Hypothesis
    The primary rules conclude from the experiment or the theory without enough strength observation condition or completed theorem statement. However, it is the pioneer to build the base of concrete system for explaining the matter world.

Essential concepts in classical mechanics

Newton's law of motion

Work and energy

Oscillation motion

  • Simple harmonic oscillator

  • Damped oscillator

  • Forced oscillator

  • Coupled oscillator

    Eigenstate and eigenvalue problem

  • N-coupled oscillator
    ​

Wave

  • Wave equation from discrete to continuous
  • Fourier series and Fourier transformation

Lagrangian

  • Least action principle
  • Symmetrical properties in space and time
  • Central field, central mass and Reduced mass
  • ​

Rotation

  • Rigid body
  • ​

Essential Math tools that you should deeply understand

  1. Basic understanding of high school math
  2. Linear algebra
    eigenstate, eigenvalue
  3. Vector calculus
    gradient, divergence, curl, Laplace
  4. Fourier Transform
    Including complex plane, phasor
  5. Calculus of Variations

Reference

Notes in this series are based on following several books, including:

  1. The Feynman Lectures on Physics
    Lots of words, but worth to read to get the concept in a easy and clear picture
  2. Classical dynamics of particles and systems
    Classic usage textbook for teaching classical dynamics in department of physics
  3. David Morin's Classical mechanics
  4. Landau Mechanics