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- catalog abstract "There are many ways of introducing the concept of probability in classical, deterministic physics. This volume is concerned with one approach, known as 'the method of arbitrary functions', which was first considered by Poincare. Essentially, the method proceeds by associating some uncertainty to our knowledge of both the initial conditions and the values of the physical constants that characterize the evolution of a physical system. By modeling this uncertainty by a probability density distribution, it is then possible to analyze how the state of the system evolves through time. This approach may be applied to a wide variety of classical problems and the author considers here examples as diverse as bouncing balls, simple and coupled harmonic oscillators, integrable systems (such as spinning tops), planetary motion, and billiards. An important aspect of this account is to study the speed of convergence for solutions in order to determine the practical relevance of the method of arbitrary functions for specific examples. Consequently, both new results on convergence, and tractable upper bounds are derived and applied.".
- catalog contributor b3570615.
- catalog created "c1992.".
- catalog date "1992".
- catalog date "c1992.".
- catalog dateCopyrighted "c1992.".
- catalog description "Includes bibliographical references (p. [151]-152) and index.".
- catalog description "There are many ways of introducing the concept of probability in classical, deterministic physics. This volume is concerned with one approach, known as 'the method of arbitrary functions', which was first considered by Poincare. Essentially, the method proceeds by associating some uncertainty to our knowledge of both the initial conditions and the values of the physical constants that characterize the evolution of a physical system. By modeling this uncertainty by a probability density distribution, it is then possible to analyze how the state of the system evolves through time. This approach may be applied to a wide variety of classical problems and the author considers here examples as diverse as bouncing balls, simple and coupled harmonic oscillators, integrable systems (such as spinning tops), planetary motion, and billiards. An important aspect of this account is to study the speed of convergence for solutions in order to determine the practical relevance of the method of arbitrary functions for specific examples. Consequently, both new results on convergence, and tractable upper bounds are derived and applied.".
- catalog extent "viii, 155 p. :".
- catalog hasFormat "Road to randomness in physical systems.".
- catalog identifier "0387977406 (New York : acid-free paper)".
- catalog identifier "3540977406 (Berlin : acid-free paper)".
- catalog isFormatOf "Road to randomness in physical systems.".
- catalog isPartOf "Lecture notes in statistics (Springer-Verlag) ; 71.".
- catalog isPartOf "Lecture notes in statistics ; 71".
- catalog issued "1992".
- catalog issued "c1992.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Road to randomness in physical systems.".
- catalog subject "519.2 20".
- catalog subject "Convergence.".
- catalog subject "Functional analysis.".
- catalog subject "Mathematical physics.".
- catalog subject "Probabilities.".
- catalog subject "QC20.7.P7 E63 1992".
- catalog subject "Statistics.".
- catalog title "A road to randomness in physical systems / Eduardo M.R.A. Engel.".
- catalog type "text".