TY  - BOOK
AU  - Gitterman,Moshe
TI  - Oscillator and Pendulum with a Random Mass
SN  - 9789814630757
U1  - 530.13 
PY  - 2015///
CY  - Singapore
PB  - World Scientific Pub. Co.
KW  - Statistical mechanics
KW  - Harmonic oscillators
KW  - Random noise theory
KW  - Pendulum
KW  - Electronic books
N1  - Includes bibliographical references (p. 139-143) and index; 1. Introduction. 1.1. 1.1 Harmonic oscillator with external noise. 1.2.  Ito-Stratonovich dilemma. 1.3. Harmonic oscillator with random frequency. 1.4. Harmonic oscillator with random damping. 1.5. Harmonic oscillator with multiplicative and additive noise. 1.6. Harmonic oscillator with a random mass. 1.7. Pendulum. 1.8. Pendulum with additive noise. 1.9. Pendulum with multiplicative noise. 1.10. Pendulum with multiplicative and additive -- 2. Oscillator with a random mass. 2.1. White and colored noise. 2.2. Birth-death process. 2.3. Piece-wise potential. 2.4. Simple treatment of correlated multiplicative and additive sources of noise. 2.5. Mass dependence instability of an oscillator with multiplicative noise. 2.6. Dichotomous randommass. 2.7. Stability of an oscillator with random mass. 2.8. Stability conditions. 2.9 Basic equations. 2.10. First moment. 2.11. White noise. 2.12. Symmetric dichotomous noise. 2.13. Asymmetric dichotomous noise. 2.14. Second moment. 2.15. Instability of the second moment. 2.16. Different stochastic models. 2.17. Probability analysis. 2.18. Diffusion of clusters with random mass. 2.19. Force-free oscillator. 2.20. Stochastic resonance in the oscillator with a randommass. 2.21. Stability conditions for a linear oscillator with a randommass. 2.22. White noise. 2.23. Dichotomous noise. 2.24. Stability conditions for a nonlinear oscillator with random damping. 2.25. Resonance phenomena. 2.26. Vibrational resonance. 2.27. Deterministic chaos -- 3. Pendulum with a random mass. 3.1. Pendulum with a random angle. 3.2. Stationary states of a pendulum. 3.3. Probabilistic approach to a deterministic pendulum. 3.4. Pendulum with random angle and random momentum. 3.5. Josephson junction with multiplicative noise. 3.6. Order and chaos: are they contradictory or complimentary? 3.7. Spring pendulum. 3.8. Analysis of nonlinear equations; Electronic reproduction; Singapore; World Scientific Publishing Co; 2015; System requirements: Adobe Acrobat Reader; Mode of access: World Wide Web; Available to subscribing institutions
N2  - Stochastic descriptions of a harmonic oscillator can be obtained by adding additive noise, or/and three types of multiplicative noise: random frequency, random damping and random mass. The first three types of noise were intensively studied in many published articles. In this book the fourth case, that of random mass, is considered in the context of the harmonic oscillator and its immediate nonlinear generalization - the pendulum. To our knowledge it is the first book fully dedicated to this problem. Two interrelated methods, the Langevin equation and the Fokker–Planck equations, as well as the Lyapunov stability method are used for the mathematical analysis. After a short introduction, the two main parts of the book describe the different properties of the random harmonic oscillator and the random pendulum with random masses. As an example, the stochastic resonance is studied, where the noise plays an unusual role, increasing the applied weak periodic signal, and also the vibration resonance in dynamic systems, where the role of noise is played by the second high-frequency periodic signal. First and second averaged moments have been calculated for a system with different types of additive and multiplicative noises, which define the stability of a system. The calculations have been extended to two multiplicative noises and to quadratic noise. This book is useful for students and scientists working in different fields of statistical physics
UR  - http://www.worldscientific.com/worldscibooks/10.1142/9352#t=toc
ER  -