Elements of Newtonian Mechanics [E-Book] : Including Nonlinear Dynamics / by Jens M. Knudsen, Poul G. Hjorth.
Knudsen, Jens M., (author)
Hjorth, Poul G., (author)
Third Revised and Enlarged Edition.
Berlin, Heidelberg : Springer, 2000
XX, 452 p. 1 illus. online resource.
englisch
9783642572340
10.1007/978-3-642-57234-0
Advanced Texts in Physics
Full Text
Table of Contents:
  • 1. The Foundation of Classical Mechanics
  • 1.1 Principia
  • 1.2 Prerequisites for Newton
  • 1.3 The Masterpiece
  • 1.4 Concluding Remarks
  • 1.5 Problems
  • 2. Newton’s Five Laws
  • 2.1 Newton’s Laws of Motion
  • 2.2 Integration of the Equation of Motion
  • 2.3 Problems
  • 3. Gravitational and Inertial Mass
  • 3.1 Gravitational Mass
  • 3.2 Inertial Mass
  • 3.3 Proportionality Between Inertial and Gravitational Mass
  • 3.4 Newtonl’s Experiment
  • 3.5 Problem
  • 4. The Galilei Transformation
  • 4.1 The Galilei Transformation
  • 4.2 Galileo Speaks
  • 4.3 Problems
  • 5. The Motion of the Earth
  • 5.1 Examples
  • 5.2 Problems
  • 6. Motion in Accelerated Reference Frames
  • 6.1 Newton’s 2nd Law Within Accelerated Reference Frames
  • 6.2 The Equivalence Principle of Mechanics
  • 6.3 The Einstein Box
  • 6.4 The Centrifugal Force
  • 6.5 Tidal Fields
  • 6.6 The Coriolis Force
  • 6.7 Tidal Forces and Local Inertial Frames
  • 6.8 The Foucault Pendulum
  • 6.9 Newton’s Bucket
  • 6.10 Review: Fictitious Forces
  • 6.11 Problems
  • 7. The Problem of Motion
  • 7.1 Kinematic and Dynamic Views of the Problem of Motion
  • 7.2 Einstein Speaks
  • 7.3 Symmetry
  • 7.4 The Symmetry (Invariance) of Newton’s 2nd Law
  • 7.5 Limited Absolute Space
  • 7.6 The Asymmetry (Variance) of Newton’s 2nd Law
  • 7.7 Critique of the Newtonian View
  • 7.8 Concluding Remarks
  • 8. Energy
  • 8.1 Work and Kinetic Energy
  • 8.2 Conservative Force Fields
  • 8.3 Central Force Fields
  • 8.4 Potential Energy and Conservation of Energy
  • 8.5 Calculation of Potential Energy
  • 8.6 The Gravitational Field Around a Homogeneous Sphere
  • 8.7 Examples
  • 8.8 Review: Conservative Forces and Potential Energy
  • 8.9 Problems
  • 9. The Center-of-Mass Theorem
  • 9.1 The Center of Mass
  • 9.2 The Center-of-Mass Frame
  • 9.3 Examples
  • 9.4 Review: Center of Mass and Center-of-Mass Theorems
  • 9.5 Comments on the Conservation Theorems
  • 9.6 Problems
  • 10. The Angular Momentum Theorem
  • 10.1 The Angular Momentum Theorem for a Particle
  • 10.2 Conservation of Angular Momentum
  • 10.3 Torque and Angular Momentum Around an Axis
  • 10.4 The Angular Momentum Theorem for a System of Particles
  • 10.5 Center of Gravity
  • 10.6 Angular Momentum Around the Center of Mass
  • 10.7 Review: Equations of Motion for a System of Particles
  • 10.8 Examples of Conservation of Angular Momentum
  • 11. Rotation of a Rigid Body
  • 11.1 Equations of Motion
  • 11.2 The Rotation Vector
  • 11.3 Kinetic Energy of a Rotating Disk
  • 11.4 Angular Momentum of an Arbitrary Rigid Body in Rotation Around a Fixed Axis
  • 11.5 Calculation of the Moment of Inertia for Simple Bodies
  • 11.6 Equation of Motion for a Rigid Body Rotating Around a Fixed Axis
  • 11.7 Work and Power in the Rotation of a Rigid Body Around a Fixed Axis
  • 11.8 The Angular Momentum Theorem Referred to Various Points
  • 11.9 Examples
  • 11.10 Review: Linear Motion and Rotation About a Fixed Axis. 266 11.11 Problems
  • 12. The Laws of Motion
  • 12.1 Review: Classical Mechanics
  • 12.2 Remarks on the Three Conservation Theorems
  • 12.3 Examples
  • 12.4 Problems
  • 13. The General Motion of a Rigid Body
  • 13.1 Inertia in Rotational Motion
  • 13.2 The Inertia Tensor
  • 13.3 Euler’s Equations
  • 13.4 Kinetic Energy
  • 13.5 Determination of the Principal Coordinate System
  • 13.6 Problems
  • 14. The Motion of the Planets
  • 14.1 Tycho Brahe
  • 14.2 Kepler and the Orbit of Mars
  • 14.3 Conic Sections
  • 14.4 Newton’s Law of Gravity Derived from Kepler’s Laws
  • 14.5 The Kepler Problem
  • 14.6 The Effective Potential
  • 14.7 The Two-Body Problem
  • 14.8 Double Stars: The Motion of the Heliocentric Reference Frame
  • 14.9 Review: Kepler Motion
  • 14.10 Examples
  • 14.11 Problems
  • 15. Harmonic Oscillators
  • 15.1 Small Oscillations
  • 15.2 Energy in Harmonic Oscillators
  • 15.3 Free Damped Oscillations
  • 15.4 Energy in Free, Weakly Damped Oscillations
  • 15.5 Forced Oscillations
  • 15.6 The Forced Damped Harmonic Oscillator
  • 15.7 Frequency Characteristics
  • 15.8 Power Absorption
  • 15.9 The Q-Value of a Weakly Damped Harmonic Oscillator
  • 15.10 The Lorentz Curve
  • 15.11 Complex Numbers
  • 15.12 Problems
  • 16. Remarks on Nonlinearity and Chaos
  • 16.1 Determinism vs Predictability
  • 16.2 Linear and Nonliner Differential Equations
  • 16.3 Phase Space
  • 16.4 A Forced, Damped Nonlinear Oscillator
  • 16.5 Liapunov Exponents
  • 16.6 Chaos in the Solar System
  • 16.7 Problems
  • Appendix. Vectors and Vector Calculus
  • Selected References
  • Answers to Problems.