Classical Mechanics
- Last updated
- Save as PDF
- Page ID
- 13940
- Book: Classical Mechanics (Tatum)
- 1: Centers of Mass
- 2: Moments of Inertia
- 2.1: Definition of Moment of Inertia
- 2.2: Meaning of Rotational Inertia
- 2.3: Moments of Inertia of Some Simple Shapes
- 2.4: Radius of Gyration
- 2.5: Plane Laminas and Mass Points distributed in a Plane
- 2.6: Three-dimensional Solid Figures. Spheres, Cylinders, Cones.
- 2.7: Three-dimensional Hollow Figures. Spheres, Cylinders, Cones
- 2.8: Torus
- 2.9: Linear Triatomic Molecule
- 2.10: Pendulums
- 2.11: Plane Laminas. Product Moment. Translation of Axes (Parallel Axes Theorem)
- 2.12: Rotation of Axes
- 2.13: Momental Ellipse
- 2.14: Eigenvectors and Eigenvalues
- 2.15: Solid Body
- 2.16: Rotation of Axes - Three Dimensions
- 2.17: Solid Body Rotation and the Inertia Tensor
- 2.18: Determination of the Principal Axes
- 2.19: Moment of Inertia with Respect to a Point
- 2.20: Ellipses and Ellipsoids
- 2.21: Tetrahedra
- 3: Systems of Particles
- 3.1: Introduction to Systems of Particles
- 3.2: Moment of Force
- 3.3: Moment of Momentum
- 3.4: Notation
- 3.5: Linear Momentum
- 3.6: Force and Rate of Change of Momentum
- 3.7: Angular Momentum
- 3.8: Torque
- 3.9: Comparison
- 3.10: Kinetic energy
- 3.11: Torque and Rate of Change of Angular Momentum
- 3.12: Torque, Angular Momentum and a Moving Point
- 3.13: The Virial Theorem
- 4: Rigid Body Rotation
- 4.1: Introduction to Rigid Body Rotation
- 4.2: Angular Velocity and Eulerian Angles
- 4.3: Kinetic Energy of Rigid Body Rotation
- 4.4: Lagrange's Equations of Motion
- 4.5: Euler's Equations of Motion
- 4.6: Force-free Motion of a Rigid Asymmetric Top
- 4.7: Nonrigid Rotator
- 4.8: Force-free Motion of a Rigid Symmetric Top
- 4.9: Centrifugal and Coriolis Forces
- 4.10: The Top
- Appendix
- 5: Collisions
- 6: Motion in a Resisting Medium
- 7: Projectiles
- 8: Impulsive Forces
- 9: Conservative Forces
- 10: Rocket Motion
- 11: Simple and Damped Oscillatory Motion
- 12: Forced Oscillations
- 13: Lagrangian Mechanics
- 13.1: Introduction to Lagrangian Mechanics
- 13.2: Generalized Coordinates and Generalized Forces
- 13.3: Holonomic Constraints
- 13.4: The Lagrangian Equations of Motion
- 13.5: Acceleration Components
- 13.6: Slithering Soap in Conical Basin
- 13.7: Slithering Soap in Hemispherical Basin
- 13.8: More Lagrangian Mechanics Examples
- 13.9: Hamilton's Variational Principle
- 14: Hamiltonian Mechanics
- 15: Special Relativity
- 15.1: Introduction
- 15.2: Preparation
- 15.3: Preparation
- 15.4: Speed is Relative - The Fundamental Postulate of Special Relativity
- 15.5: The Lorentz Transformations
- 15.6: But This Defies Common Sense
- 15.7: The Lorentz Transformation as a Rotation
- 15.8: Timelike and Spacelike 4-Vectors
- 15.9: The FitzGerald-Lorentz Contraction
- 15.10: Time Dilation
- 15.11: The Twins Paradox
- 15.12: A, B and C
- 15.13: Simultaneity
- 15.14: Order of Events, Causality and the Transmission of Information
- 15.15: Derivatives
- 15.16: Addition of Velocities
- 15.17: Aberration of Light
- 15.18: Doppler Effect
- 15.19: The Transverse and Oblique Doppler Effects
- 15.20: Acceleration
- 15.21: Mass
- 15.22: Momentum
- 15.23: Some Mathematical Results
- 15.24: Kinetic Energy
- 15.25: Addition of Kinetic Energies
- 15.26: Energy and Mass
- 15.27: Energy and Momentum
- 15.28: Units
- 15.29: Force
- 15.2: The Speed of Light
- 15.30: Electromagnetism
- 16: Hydrostatics
- 17: Vibrating Systems
- 17.1: Introduction
- 17.2: The Diatomic Molecule
- 17.3: Two Masses, Two Springs and a Brick Wall
- 17.4: Double Torsion Pendulum
- 17.5: Double Pendulum
- 17.6: Linear Triatomic Molecule
- 17.7: Two Masses, Three Springs, Two brick Walls
- 17.8: Transverse Oscillations of Masses on a Taut String
- 17.9: Vibrating String
- 17.10: Water
- 17.11: A General Vibrating System
- 17.12: A Driven System
- 17.13: A Damped Driven System
- 18: The Catenary
- 19: The Cycloid
- 19.1: Introduction
- 19.2: Tangent to the Cycloid
- 19.3: The Intrinsic Equation to the Cycloid
- 19.4: Variations
- 19.5: Motion on a Cycloid, Cusps Up
- 19.6: Motion on a Cycloid, Cusps Down
- 19.7: The Brachystochrone Property of the Cycloid
- 19.8: Contracted and Extended Cycloids
- 19.9: The Cycloidal Pendulum
- 19.10: Examples of Cycloidal Motion in Physics
- 20: Miscellaneous
- 21: Central Forces and Equivalent Potential
- 22: Dimensions
- Book: Variational Principles in Classical Mechanics (Cline)
- Prologue
- 1: A brief History of Classical Mechanics
- 2: Review of Newtonian Mechanics
- 2.1: Introduction to Newtonian Mechanics
- 2.2: Newton's Laws of motion
- 2.3: Inertial Frames of reference
- 2.4: First-order Integrals in Newtonian mechanics
- 2.5: Conservation laws in classical mechanics
- 2.6: Motion of finite-sized and many-body systems
- 2.7: Center of Mass of a many-body system
- 2.8: Total Linear Momentum of a Many-body System
- 2.9: Angular Momentum of a Many-Body System
- 2.10: Work and Kinetic Energy for a Many-Body System
- 2.11: Virial Theorem
- 2.12: Applications of Newton's Equations of Motion
- 2.13 Solution of many-body equations of motion
- 2.14: Newton's Law of Gravitation
- 2.E: Review of Newtonian Mechanics (Exercises)
- 2.i Workshop exercises
- 2.S: Newtonian Mechanics (Summary)
- 3: Linear Oscillators
- 3.1: Introduction to Linear Oscillators
- 3.2: Linear Restoring Forces
- 3.3: Linearity and Superposition
- 3.4: Geometrical Representations of Dynamical Motion
- 3.5: Linearly-damped Free Linear Oscillator
- 3.6: Sinusoidally-drive, linearly-damped, linear oscillator
- 3.7: Wave equation
- 3.8: Travelling and standing wave solutions of the wave equation
- 3.9: Waveform Analysis
- 3.10: Signal Processing
- 3.11: Wave propagation
- 3.S: Linear Oscillators (Summary)
- 12: Coupled Linear Oscillators
- 13: Hamilton’s Principle of Least Action
- 13.1: Introduction to Hamilton’s Principle of Least Action
- 13.2: Principle of Least Action
- 13.3: Standard Lagrangian
- 13.4: Gauge Invariance of the Lagrangian
- 13.5: Non-Standard Lagrangians
- 13.6: Inverse Variational Calculus
- 13.7: Dissipative Lagrangians
- 13.8: Linear Velocity-Dependent Dissipation
- 13.S: Hamilton’s Principle of Least Action (Summary)
Mon, 09 Apr 2018 15:28:51 GMT
Classical Mechanics
Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies. If the present state of an object is known it is possible to predict by the laws of classical mechanics how it will move in the future (determinism) and how it has moved in the past (reversibility).
Thumbnail: Proper Euler angles geometrical definition. The xyz (fixed) system is shown in blue, the XYZ (rotated) system is shown in red. The line of nodes (N) is shown in green. Image used with permission (CC BY 3.0; Lionel Brits).