Simulations of oscillatory systems. (2015)

• Record Type: Book
• Further Information: Note: Eugene I. Butikov.
• Authors: Butikov, E. I (Evgeniĭ Ivanovich)
• Contents: 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
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2015
• Extent: 1 online resource, illustrations
• Subjects: 530.416; Oscillations; Oscillations -- Mathematics; Oscillations -- Data processing
• Languages: English
• ISBNs: 9781498707701; 9781498717144
• Related ISBNs: 9781498707688
• Notes: Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.