Book chapter
Index Two: Impact Problems
Dynamics with Inequalities, pp.207-272
Other Titles in Applied Mathematics, Society for Industrial and Applied Mathematics
01/01/2011
DOI: 10.1137/1.9781611970715.ch6
Abstract
Mechanical impact problems are a rich source of finite-dimensional and infinite-dimensional DVIs. Unlike resource-constrained problems, these are all at least formally index two since Newton's laws of motion give second order differential equations.
We distinguish between rigid-body dynamics with impact, which give finite-dimensional problems, and elastic-body dynamics with impact, which give infinite-dimensional problems. For elastic-body dynamics there can be contact over the domain of the body, or over all or part of the boundary of the body. Also, a body can be elastic or viscoelastic. For the infinite-dimensional problems, the regularity of the solution both in time and space can be crucial for the existence of solutions and their behavior.
If the (normal) contact force is known, then determining the Coulomb friction forces and the resulting motions can be represented as an index-one problem of a variational kind. However, with both the normal and the Coulomb friction forces to be determined, the problems can no longer be represented as optimization problems. Impact problems with Coulomb friction remain the most challenging problems involving mechanics with constraints.
Details
- Title: Subtitle
- Index Two: Impact Problems
- Creators
- David E Stewart - University of Iowa
- Resource Type
- Book chapter
- Publication Details
- Dynamics with Inequalities, pp.207-272
- Publisher
- Society for Industrial and Applied Mathematics
- Series
- Other Titles in Applied Mathematics
- DOI
- 10.1137/1.9781611970715.ch6
- Language
- English
- Date published
- 01/01/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984242342402771
Metrics
6 Record Views