Ebook: Set-Valued Force Laws: Dynamics of Non-Smooth Systems

As one of the oldest natural sciences, mechanics occupies a certain pioneering role in determining the development of exact sciences through its interaction with mathematics. As a matter of fact, there is hardly an area in mathematics that hasn't found an application of some form in mechanics. It is thus almost inevitable that theoretical methods in mechanics are highly developed and laid out on different levels of abstraction. With the spread of digital processors this goes as far as the implementation in commercial computer codes, where the user is merely con­ fronted on the surface with the processes that run in the background, i. e. mechan­ ics as such: in teaching and research, as well as in the context of industry, me­ chanics is much more, and must remain much more than the mere production of data with the help of a processor. Mechanics, as it is talked about here, tradition­ ally includes a wide spectrum, ranging from applied mechanics, analytical and technical mechanics to modeling. and experimental mechanics, as well as technical realization. It also includes the subdisciplines of rigid body mechanics, continuum mechanics, or fluid mechanics, to mention only a few. One of the fundamental and most important concepts used by nearly all natural sciences is the concept of linearization, which assumes the differentiability of mappings. As a matter of fact, all of classical mechanics is based on the avail­ ability of this quality.

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This is one out of a few books which treat the dynamics of non-smooth systems in finite degree of freedom mechanics. Based on the classical multibody system approach set-valued force laws are introduced to fully encompass situations like the frictional contact problem, unilateral constraints, the behavior of one-way clutches, and even velocity jumps not related to any kind of collisions. The book concentrates on modern mathematical methods and concepts from optimization theory combined with classical analytical mechanics, such that it should be valuable for people working on discontinuity problems in nearly all branches of classical physics.

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This is one out of a few books which treat the dynamics of non-smooth systems in finite degree of freedom mechanics. Based on the classical multibody system approach set-valued force laws are introduced to fully encompass situations like the frictional contact problem, unilateral constraints, the behavior of one-way clutches, and even velocity jumps not related to any kind of collisions. The book concentrates on modern mathematical methods and concepts from optimization theory combined with classical analytical mechanics, such that it should be valuable for people working on discontinuity problems in nearly all branches of classical physics.
Content:
Front Matter....Pages i-ix
Introduction....Pages 1-16
Fundamental Concepts....Pages 17-31
Rigid Body Systems....Pages 33-53
Motion and Discontinuity Events....Pages 55-67
Displacement and Velocity Potentials....Pages 69-77
Representation of Scalar Force Laws....Pages 79-90
Force Laws on Different Kinematic Levels....Pages 91-101
Index Sets and LCP-Formulation....Pages 103-115
Principles in Dynamics....Pages 117-129
Spatial Coulomb Friction....Pages 131-154
Velocity Jumps due to C 0-Constraints....Pages 155-173
Electropneumatic Drilling Machine....Pages 175-182
Percussion Drilling Machine....Pages 183-193
Turbine Blade Damper....Pages 195-203
Concluding Remarks....Pages 205-208
Back Matter....Pages 209-222

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This is one out of a few books which treat the dynamics of non-smooth systems in finite degree of freedom mechanics. Based on the classical multibody system approach set-valued force laws are introduced to fully encompass situations like the frictional contact problem, unilateral constraints, the behavior of one-way clutches, and even velocity jumps not related to any kind of collisions. The book concentrates on modern mathematical methods and concepts from optimization theory combined with classical analytical mechanics, such that it should be valuable for people working on discontinuity problems in nearly all branches of classical physics.
Content:
Front Matter....Pages i-ix
Introduction....Pages 1-16
Fundamental Concepts....Pages 17-31
Rigid Body Systems....Pages 33-53
Motion and Discontinuity Events....Pages 55-67
Displacement and Velocity Potentials....Pages 69-77
Representation of Scalar Force Laws....Pages 79-90
Force Laws on Different Kinematic Levels....Pages 91-101
Index Sets and LCP-Formulation....Pages 103-115
Principles in Dynamics....Pages 117-129
Spatial Coulomb Friction....Pages 131-154
Velocity Jumps due to C 0-Constraints....Pages 155-173
Electropneumatic Drilling Machine....Pages 175-182
Percussion Drilling Machine....Pages 183-193
Turbine Blade Damper....Pages 195-203
Concluding Remarks....Pages 205-208
Back Matter....Pages 209-222
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