Isbn: 9789819575602 - a billiard problem in nonlinear dissipative systems: 18 (surveys and tutorials in the applied mathematical sciences, 18) (12 resultados)

Paperback. Condición: new. Paperback. This book addresses a new class of billiard problems, focusing on the motion of a self-propelling disk in a nonlinear dissipative system on a rectangular domain. Unlike classical billiards, which have been extensively studied in mathematics, this setting introduces unique dynamics inspired by experiments with camphor disks floating on watera well-known phenomenon in nonlinear science. Laboratory observations reveal two striking properties: (i) the disk reflects without physical collision at the boundary, and (ii) the reflection angle exceeds the incidence angle, differing from the perfect elastic reflection of classical billiards. These features suggest that the behavior of a self-propelling disk is fundamentally distinct from classical billiard motion.The purpose of this book is to provide a mathematical understanding of such dynamics. We propose three levels of modeling: a moving-boundary (MB) model, a particle model, and a discrete-time model. To demonstrate that the MB model satisfies properties (i) and (ii), we derive the particle model for slow disk motion, describing its position and velocity. Numerical simulations indicate that although classical billiards in a rectangle are simple, the particle model exhibits complex behavior depending on the domains shape. To analyze this complexity, we construct discrete-time models that capture the evolution of reflection angles and positions. Using dynamical systems theory, bifurcation analysis, and complementary numerical methods, we show that a self-propelling disk can display intricate and varied billiard motionseven in a rectangular domaindue to angle interactions.This book emphasizes that the trajectory of a billiard disk in a nonlinear dissipative system is determined by inherent dynamics, unlike classical billiards, where outcomes depend heavily on player skill. We propose three levels of modeling: a moving-boundary (MB) model, a particle model, and a discrete-time model. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.…

Paperback. Condición: new. Paperback. This book addresses a new class of billiard problems, focusing on the motion of a self-propelling disk in a nonlinear dissipative system on a rectangular domain. Unlike classical billiards, which have been extensively studied in mathematics, this setting introduces unique dynamics inspired by experiments with camphor disks floating on watera well-known phenomenon in nonlinear science. Laboratory observations reveal two striking properties: (i) the disk reflects without physical collision at the boundary, and (ii) the reflection angle exceeds the incidence angle, differing from the perfect elastic reflection of classical billiards. These features suggest that the behavior of a self-propelling disk is fundamentally distinct from classical billiard motion.The purpose of this book is to provide a mathematical understanding of such dynamics. We propose three levels of modeling: a moving-boundary (MB) model, a particle model, and a discrete-time model. To demonstrate that the MB model satisfies properties (i) and (ii), we derive the particle model for slow disk motion, describing its position and velocity. Numerical simulations indicate that although classical billiards in a rectangle are simple, the particle model exhibits complex behavior depending on the domains shape. To analyze this complexity, we construct discrete-time models that capture the evolution of reflection angles and positions. Using dynamical systems theory, bifurcation analysis, and complementary numerical methods, we show that a self-propelling disk can display intricate and varied billiard motionseven in a rectangular domaindue to angle interactions.This book emphasizes that the trajectory of a billiard disk in a nonlinear dissipative system is determined by inherent dynamics, unlike classical billiards, where outcomes depend heavily on player skill. We propose three levels of modeling: a moving-boundary (MB) model, a particle model, and a discrete-time model. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.…

Taschenbuch. Condición: Neu. A Billiard Problem in Nonlinear Dissipative Systems | Tomoyuki Miyaji (u. a.) | Taschenbuch | Surveys and Tutorials in the Applied Mathematical Sciences | xii | Englisch | 2026 | Springer | EAN 9789819575602 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. …

Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book addresses a new class of billiard problems, focusing on the motion of a self-propelling disk in a nonlinear dissipative system on a rectangular domain. Unlike classical billiards, which have been extensively studied in mathematics, this setting introduces unique dynamics inspired by experiments with camphor disks floating on water a well-known phenomenon in nonlinear science. Laboratory observations reveal two striking properties: (i) the disk reflects without physical collision at the boundary, and (ii) the reflection angle exceeds the incidence angle, differing from the perfect elastic reflection of classical billiards. These features suggest that the behavior of a self-propelling disk is fundamentally distinct from classical billiard motion.The purpose of this book is to provide a mathematical understanding of such dynamics. We propose three levels of modeling: a moving-boundary (MB) model, a particle model, and a discrete-time model. To demonstrate that the MB model satisfies properties (i) and (ii), we derive the particle model for slow disk motion, describing its position and velocity. Numerical simulations indicate that although classical billiards in a rectangle are simple, the particle model exhibits complex behavior depending on the domain s shape. To analyze this complexity, we construct discrete-time models that capture the evolution of reflection angles and positions. Using dynamical systems theory, bifurcation analysis, and complementary numerical methods, we show that a self-propelling disk can display intricate and varied billiard motions even in a rectangular domain due to angle interactions.This book emphasizes that the trajectory of a billiard disk in a nonlinear dissipative system is determined by inherent dynamics, unlike classical billiards, where outcomes depend heavily on player skill.…

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Paperback. Condición: new. Paperback. This book addresses a new class of billiard problems, focusing on the motion of a self-propelling disk in a nonlinear dissipative system on a rectangular domain. Unlike classical billiards, which have been extensively studied in mathematics, this setting introduces unique dynamics inspired by experiments with camphor disks floating on watera well-known phenomenon in nonlinear science. Laboratory observations reveal two striking properties: (i) the disk reflects without physical collision at the boundary, and (ii) the reflection angle exceeds the incidence angle, differing from the perfect elastic reflection of classical billiards. These features suggest that the behavior of a self-propelling disk is fundamentally distinct from classical billiard motion.The purpose of this book is to provide a mathematical understanding of such dynamics. We propose three levels of modeling: a moving-boundary (MB) model, a particle model, and a discrete-time model. To demonstrate that the MB model satisfies properties (i) and (ii), we derive the particle model for slow disk motion, describing its position and velocity. Numerical simulations indicate that although classical billiards in a rectangle are simple, the particle model exhibits complex behavior depending on the domains shape. To analyze this complexity, we construct discrete-time models that capture the evolution of reflection angles and positions. Using dynamical systems theory, bifurcation analysis, and complementary numerical methods, we show that a self-propelling disk can display intricate and varied billiard motionseven in a rectangular domaindue to angle interactions.This book emphasizes that the trajectory of a billiard disk in a nonlinear dissipative system is determined by inherent dynamics, unlike classical billiards, where outcomes depend heavily on player skill. We propose three levels of modeling: a moving-boundary (MB) model, a particle model, and a discrete-time model. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.…

Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book addresses a new class of billiard problems, focusing on the motion of a self-propelling disk in a nonlinear dissipative system on a rectangular domain. Unlike classical billiards, which have been extensively studied in mathematics, this setting introduces unique dynamics inspired by experiments with camphor disks floating on water a well-known phenomenon in nonlinear science. Laboratory observations reveal two striking properties: (i) the disk reflects without physical collision at the boundary, and (ii) the reflection angle exceeds the incidence angle, differing from the perfect elastic reflection of classical billiards. These features suggest that the behavior of a self-propelling disk is fundamentally distinct from classical billiard motion.The purpose of this book is to provide a mathematical understanding of such dynamics. We propose three levels of modeling: a moving-boundary (MB) model, a particle model, and a discrete-time model. To demonstrate that the MB model satisfies properties (i) and (ii), we derive the particle model for slow disk motion, describing its position and velocity. Numerical simulations indicate that although classical billiards in a rectangle are simple, the particle model exhibits complex behavior depending on the domain s shape. To analyze this complexity, we construct discrete-time models that capture the evolution of reflection angles and positions. Using dynamical systems theory, bifurcation analysis, and complementary numerical methods, we show that a self-propelling disk can display intricate and varied billiard motions even in a rectangular domain due to angle interactions.This book emphasizes that the trajectory of a billiard disk in a nonlinear dissipative system is determined by inherent dynamics, unlike classical billiards, where outcomes depend heavily on player skill. 138 pp. Englisch.…

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Taschenbuch. Condición: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book addresses a new class of billiard problems, focusing on the motion of a self-propelling disk in a nonlinear dissipative system on a rectangular domain. Unlike classical billiards, which have been extensively studied in mathematics, this setting introduces unique dynamics inspired by experiments with camphor disks floating on watera well-known phenomenon in nonlinear science. Laboratory observations reveal two striking properties: (i) the disk reflects without physical collision at the boundary, and (ii) the reflection angle exceeds the incidence angle, differing from the perfect elastic reflection of classical billiards. These features suggest that the behavior of a self-propelling disk is fundamentally distinct from classical billiard motion.The purpose of this book is to provide a mathematical understanding of such dynamics. We propose three levels of modeling: a moving-boundary (MB) model, a particle model, and a discrete-time model. To demonstrate that the MB model satisfies properties (i) and (ii), we derive the particle model for slow disk motion, describing its position and velocity. Numerical simulations indicate that although classical billiards in a rectangle are simple, the particle model exhibits complex behavior depending on the domain's shape. To analyze this complexity, we construct discrete-time models that capture the evolution of reflection angles and positions. Using dynamical systems theory, bifurcation analysis, and complementary numerical methods, we show that a self-propelling disk can display intricate and varied billiard motionseven in a rectangular domaindue to angle interactions.This book emphasizes that the trajectory of a billiard disk in a nonlinear dissipative system is determined by inherent dynamics, unlike classical billiards, where outcomes depend heavily on player skill.Springer Nature Customer Service Center GmbH, Europaplatz 3, 69115 Heidelberg 152 pp. Englisch.…

Condición: New. Print on Demand.

Condición: New. PRINT ON DEMAND.