https://murray.cds.caltech.edu/index.php?title=Aspects_of_Geometric_Mechanics_and_Control_of_Mechanical_Systems&feed=atom&action=historyAspects of Geometric Mechanics and Control of Mechanical Systems - Revision history2021-10-25T23:36:50ZRevision history for this page on the wikiMediaWiki 1.35.3https://murray.cds.caltech.edu/index.php?title=Aspects_of_Geometric_Mechanics_and_Control_of_Mechanical_Systems&diff=20048&oldid=prevMurray: htdb2wiki: creating page for 1995_adl95-phd.html2016-05-15T06:20:39Z<p>htdb2wiki: creating page for 1995_adl95-phd.html</p>
<p><b>New page</b></p><div>{{HTDB paper<br />
| authors = Andrew D. Lewis<br />
| title = Aspects of Geometric Mechanics and Control of Mechanical Systems<br />
| source = PhD Dissertation, Caltech, Jun 1995<br />
| year = <br />
| type = CDS Technical Report<br />
| funding = NSF<br />
| url = http://www.cds.caltech.edu/~murray/preprints/adl95-phd.pdf<br />
| abstract = <br />
any interesting control systems are mechanical control systems. In spite of<br />
this, there has not been much effort to develop methods which use the special<br />
structure of mechanical systems to obtain analysis tools which are<br />
suitable for these systems. In this dissertation we take the first steps<br />
towards a methodical treatment of mechanical control systems.<br />
<p><br />
First we develop a framework for analysis of certain classes of<br />
mechanical control systems. In the Lagrangian formulation we study ``simple<br />
mechanical control systems'' whose Lagrangian is ``kinetic energy minus<br />
potential energy.'' We propose a new and useful definition of<br />
controllability for these systems and obtain a computable set of conditions<br />
for this new version of controllability. We also obtain decompositions of<br />
simple mechanical systems in the case when they are not controllable. In the<br />
Hamiltonian formulation we study systems whose control vector fields are<br />
Hamiltonian. We obtain decompositions which describe the controllable and<br />
uncontrollable dynamics. In each case, the dynamics are shown to be<br />
Hamiltonian in a suitably general sense.<br />
<p><br />
Next we develop intrinsic descriptions of Lagrangian and Hamiltonian<br />
mechanics in the presence of external inputs. This development is a first<br />
step towards a control theory for general Lagrangian and Hamiltonian<br />
control systems. Systems with constraints are also studied. We first give a<br />
thorough overview of variational methods including a comparison of the<br />
``nonholonomic'' and ``vakonomic'' methods. We also give a generalised<br />
definition for a constraint and, with this more general definition, we are<br />
able to give some preliminary controllability results for constrained systems.<br />
<br />
| flags = NoRequest<br />
| tag = adl95-phd<br />
| id = 1995<br />
}}</div>Murray