Classical mechanics

From Physics wiki

Introduction

• Prerequisites

Kinematics

• Position
• Velocity
• Acceleration
• Angular frequency
• Angular acceleration
• Centripetal acceleration

Newtonian mechanics

Fundamentals Momentum Inertia Newton's first law Force Newton's second law Newton's third law Work Hooke's law Tension Conservation Inertial reference frame Galilean invariance Conservation of momentum Impulse Work-energy theorem Potential energy Conservation of energy Friction Collision

Rotation Centripetal force Angular momentum Torque Moment of inertia (list of moments of inertia) Rotational kinetic energy Torsion pendulum Gravity Weight Inclined plane Simple pendulum Physical pendulum Projectile motion Constraints Constraints Virtual displacement Virtual work Statics Static equilibrium Simple machines

Lagrangian mechanics

• Generalized coordinates
• d'Alembert's principle (principle of virtual work)
• Euler-Lagrange equations
• Lagrangian
• Hamilton's principle
• Cyclic variables
• Noether's theorem
• Kinematics in spherical coordinates
• Kinematics in cylindrical coordinates

Advanced:

• Reparameterization invariance

Hamiltonian dynamics

• Hamiltonian
• Hamilton's equations
• Poisson bracket
• Canonical transformations
• Generalized Hamiltonian dynamics
• Routh's procedure
• Maupertuis' principle
• Hamilton-Jacobi equation
• Liouville's theorem

Central force motion

• Central force
• Reduction from two-body to one-body problem
• Effective potential
• Isotropic harmonic oscillator
• Inverse square-law force (Kepler problem)
• Kepler's laws of planetary motion
  • Kepler's first law
  • Kepler's second law
  • Kepler's third law
• Laplace-Runge-Lenz vector
• Exercises

Non-inertial reference frames

• Rotating frame
• Angular velocity
• Fictitious force

Models

• Foucault pendulum

Rigid body dynamics

• Rigid body

• Moment of inertia tensor (list of moment of inertia tensors)
• Torque
• Euler's equations
• Precession
• Poinsot's construction
• Euler angles

Models

• Heavy symmetrical top

Gravitational potential theory

• Gravitational potential of an extended body

Models

• Precession of the equinoxes

Oscillations and Vibrations

• Harmonic approximation
• Modal analysis

Models

• Vibrating string (Continuum mechanics)

Perturbation theory

Many body problem

Related subjects

• Continuum mechanics (subject)
• Classical field theory (subject)
• Chaos (subject)
• Quantum mechanics (subject)

Resources

• Books
• Websites
• Formulae