Constraint analysis for variational discrete systems

Multiscale analysis for nonlinear variational problems arising from discrete systems

The object of this thesis is the study of high density discrete systems as variational limit of low density discrete energies indexed by the number of nodes of the system itself. In this context the term discreteness should be understood rather broadly as inferring to different scales from crystal lattice to grain structure while the low-to-high density limit refers to the discrete-to-continuum...

Robinson Stability of Parametric Constraint Systems via Variational Analysis

Analysis of Discrete-Time Linear Switched Systems: A Variational Approach

A powerful approach for analyzing the stability of continuous–time switched systems is based on using tools from optimal control theory to characterize the “most unstable” switching law. This reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific “most unstable” switching law. More generally, this so–called variational approach was success...

Incremental Constraint Satisfaction for Variational Design Systems 1

Variational Design is a general and powerful technique for supporting the preliminary stages of a design. It allows the coupling of engineering constraints and geometric constraints by converting them into a system of equations. Such a facility provides the user with appropriate tools to explore design alternatives during the early design stages. However, algorithms employed by the current vari...

Variational Discrete Dirac Mechanics—implicit Discrete Lagrangian and Hamiltonian Systems

We construct discrete analogues of Tulczyjew’s triple and induced Dirac structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving implicit discrete Lagrangian and Hamiltonian systems, while incorporating discrete Dirac constraints. In particular, this yields implicit nonholonomic Lagrangia...