Classical Mechanics
Basics
Speed and Acceleration
- Position, Speed, Acceleration
- Cartesian Coordinate System
- Polar Coordinate System
- Cylindrical Coordinate System
- Spherical Coordinate System
Various Motions
Newtonian Mechanics and Linear Motion of Particles
- Newton’s Laws of Motion $\mathbf{F} = \dfrac{d \mathbf{p}}{dt} = m\mathbf{a}$
- Definition of Mass, Force, Momentum $m$, $\mathbf{F}$, $\mathbf{p}$
- Definition of Kinetic Energy, Potential Energy in Physics
- Work, Work-Energy Theorem
- Angular Momentum and Torque
Oscillation
- Restoring Force and 1D Simple Harmonic Oscillator
- Damped Harmonic Oscillation
- Forced Harmonic Oscillation and Resonance Frequency
- Coupled Oscillation
- Multiple Spring Oscillation
Non-Inertial Reference Frames
Gravity and Central Forces
Motion of Particle Systems
- Center of Mass and Linear Momentum of a Particle System
- Angular Momentum of a Particle System
- Kinetic Energy of a Particle System
Variable Mass
- Equation of Motion for Variable Mass Systems
- Tsiolkovsky’s Rocket Equation $\mathbf{v} = \mathbf{v}_{0} + \mathbf{v} \ln \dfrac{m_{0}}{m}$
- Mass Dependent on Position: Motion of a Ball Connected to a Chain
Motion of Rigid Bodies
- Moment of Inertia and Radius of Gyration
- Theorem of Perpendicular Axes
- Parallel Axis Theorem
- Physical Pendulum
Lagrangian Mechanics
- Degrees of Freedom
- Constraint Conditions
- Generalized Coordinates
- Lagrangian Mechanics and Hamilton’s Principle of Least Action
- Euler-Lagrange Equation in Physics
Miscellaneous
References
- Grant R. Fowles and George L. Cassiday, Analytical Mechanics (7th Edition, 2005)
All posts
- Parabolic Motion: Horizontal Range and Maximum Height Angle
- Velocity and Acceleration in Polar Coordinates
- Velocity and Acceleration in Cylindrical Coordinates
- Velocity and Acceleration in a Coordinate System
- Velocity and Acceleration in Cartesian Coordinate System
- Inertia Moment and Turning Radius
- Inertia Moment of a Thin Rod
- Parallel Axis Theorem
- Vertical Axis Theorem
- Inertia Moments of Disks and Cylinders
- Moment of Inertia of a Ring and Cylindrical Shell
- Sphere's Moment of Inertia
- Kinetic and Potential Energy Definitions in Physics
- Moment of Inertia of a Spherical Shell
- Restoring Force and One-Dimensional Simple Harmonic Oscillator
- Lagrangian Mechanics and Hamiltons Variational Principle
- Euler-Lagrange Equation in Physics
- Velocity and Acceleration of an Object Moving in a Rotating Coordinate System
- Center of Mass and Linear Momentum of a Particle System
- Newton's Laws of Motion
- Physics: The Definition of Mass, Force, and Momentum
- The Reason Why Momentum is Denoted by p
- Angular Momentum and Torque
- Angular Momentum of Particle Systems
- Centrifugal Force
- Kinetic Energy of Particle Systems
- Law of Universal Gravitation: Gravity
- Kepler's Laws of Planetary Motion
- Uniform Sphere Shell and the Gravity of a Separated Particle
- Kepler's Second Law: The Law of Equal Areas
- Orbit Equation of a Particle under Central Force
- Kepler's First Law: The Law of Elliptical Orbits
- Kepler's Third Law: The Harmony of the Worlds
- Day, Work-Energy Theorem
- Damped Harmonic Oscillation
- Forced Harmonic Vibration and Resonant Frequency
- Physical Pendulum
- Coupled Oscillations
- Multiple Spring Oscillation
- Equations of Motion for a Variable Mass System
- Tsiolkovsky Rocket Equation
- Mass Dependent on Position: The Motion of Balls Connected by Chains
- Position, Velocity, and Acceleration
- Free Fall Motion
- What is Degrees of Freedom in Physics?
- What is a Constraint in Physics?