Butikov Simulations of Oscillatory Systems

with Award-Winning Software, Physics of Oscillations
Erscheinungsjahr 2015
ISBN: 978-1-4987-0770-1
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 363 Seiten

Deepen Your Students’ Understanding of Oscillations through Interactive Experiments

Simulations of Oscillatory Systems: with Award-Winning Software, Physics of Oscillations provides a hands-on way of visualizing and understanding the fundamental concepts of the physics of oscillations. Both the textbook and software are designed as exploration-oriented supplements for courses in general physics and the theory of oscillations.

The book is conveniently structured according to mathematical complexity. Each chapter in Part I contains activities, questions, exercises, and problems of varying levels of difficulty, from straightforward to quite challenging. Part II presents more sophisticated, highly mathematical material that delves into the serious theoretical background for the computer-aided study of oscillations.

The software package allows students to observe the motion of linear and nonlinear mechanical oscillatory systems and to obtain plots of the variables that describe the systems along with phase diagrams and plots of energy transformations. These computer simulations provide clear, vivid illustrations of oscillations in various physical systems, bringing to life many abstract concepts, developing students’ physical intuition, and complementing the analytical study of the subject. Students can investigate phenomena that would otherwise be difficult to study in a more conventional manner.

Autoren/Hrsg.

Butikov, Eugene I.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein

Inhaltsverzeichnis

Introduction

Oscillations in Simple Systems

Free Oscillations of a Linear Oscillator

Summary of the Theory

Review of the Principal Formulas

Questions, Problems, Suggestions

Torsion Spring Oscillator with Dry Friction

Summary of the Theory
Review of the Principal Formulas

Questions, Problems, Suggestions

Forced Oscillations in a Linear System

Summary of the Theory

Steady-State Forced Oscillations

Transient Processes

Review of the Principal Formulas

Questions, Problems, Suggestions

Square-Wave Excitation of a Linear Oscillator

Theoretical Background

Steady-State Forced Oscillations under the Square-Wave Torque

Transient Processes under the Square-Wave External Torque

Estimation of the Amplitude of Steady-State Oscillations
Energy Transformations

The Electromagnetic Analogue of the Mechanical System

Concluding Remarks

Review of the Principal Formulas

Questions, Problems, Suggestions

Parametric Excitation of Oscillations

Summary of the Theory. General Concepts
Frequency Ranges of Parametric Excitation

Concluding Remarks

Questions, Problems, Suggestions

Sinusoidal Modulation of the Parameter

Summary of the Theory: Basic Concepts

The Intervals of Parametric Instability

Concluding Remarks

Questions, Problems, Suggestions

Nonlinear Oscillations

Free Oscillations of the Rigid Pendulum

Summary of the Theory

Oscillations of the Pendulum with Extremely Large Amplitudes

Period of Revolutions and Large Oscillations

The Influence of Friction

Review of the Principal Formulas

Questions, Problems, Suggestions

Rigid Planar Pendulum under Sinusoidal Forcing

Regular Response of a Harmonically Driven Rigid Pendulum

Steady-State Response-Frequency Curves
Subharmonic and Superharmonic Resonances

Other Extraordinary Regular Forced Oscillations

Concluding Remarks

Pendulum with a Square-Wave Modulated Length

The Investigated Physical System
The Threshold of Parametric Excitation
Autoresonance, Bifurcations, Multistability
Quantitative Theory of Parametric Excitation
Frequency Ranges for Parametric Resonance
Intervals of Parametric Excitation in the Presence of Friction

Concluding Remarks

Rigid Pendulum with Oscillating Pivot

Introductory Notes

Kapitza’s Pendulum— Dynamic Stabilization

The Physical Model of the Investigated System

Parametric Resonance

Physical Reasons for Stability of the Inverted Pendulum

An Approximate Quantitative Theory of the Inverted Pendulum
Exact Differential Equation for Pendulum with Oscillating Pivot

Effective Potential Function for a Pendulum

Subharmonic Resonances of High Orders
Upper Boundary of Dynamic Stability

Enhanced Criterion for Kapitza’s Pendulum Stability
Complicated Regular Motions of the Parametrically Driven Pendulum

Chaotic Motions of the Pendulum

Concluding Remarks

Torsion Pendulum with Dry and Viscous Damping

Basics of the Theory

Sinusoidally Driven Oscillator with Dry Friction

Excitation at Sub-Resonant Frequencies

Concluding Remarks

Bibliography

Index

Über Autor(innen)

Eugene I. Butikov is a professor of physics at St. Petersburg State University. His work focuses on solid-state physics and the theory of nonlinear oscillations as well as developing interactive educational software for university-level physics students.