## Search

Now showing items 1-10 of 13

#### Configuration controllability of simple mechanical control systems

(Society for Industrial and Applied Mathematics, 1995)

In this paper we present a definition of "configuration controllability" for
mechanical systems whose Lagrangian is kinetic energy with respect to a
Riemannian metric minus potential energy. A computable test for this ...

#### Aspects of Geometric Mechanics and Control of Mechanical Systems

(1995)

Many interesting control systems are mechanical control systems. In spite of
this, there has not been much effort to develop methods which use the special
structure of mechanical systems to obtain analysis tools which ...

#### Affine connections and distributions

(1996)

We investigate various aspects of the interplay of an affine connection with
a distribution. When the affine connection restricts to the distribution, we
discuss torsion, curvature, and holonomy of the affine connection. ...

#### Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems

(D. Reidel, 1992)

In this Letter, a Lagrangian foliation of the zero energy level is constructed for a family of planar central force problems. The dynamics on the leaves are explicitly computed and these dynamics are given a simple ...

#### Nonholonomic mechanics and locomotion: the snakeboard example

(IEEE, 1994)

Analysis and simulations are performed for a simplified model of a commercially available variant on the skateboard, known as the Snakeboard.1 Although the model exhibits basic gait patterns seen in a large number of ...

#### The geometry of the Gibbs-Appell equations and Gauss's Principle of Least Constraint

(1995)

We present a generalisation of the Gibbs-Appell equations which is valid
for general Lagrangians. The general form of the Gibbs-Appell equations is
shown to be valid in the case when constraints and external forces ...

#### Energy-preserving affine connections

(1997)

A Riemannian affine connection on a Riemannian manifold has the property that
is preserves the ``kinetic energy'' associated with the metric. However,
there are other affine connections which have this property, and ...

#### Decompositions of control systems on manifolds with an affine connection

(North-Holland, 1997)

In this letter we present a decomposition for control systems whose drift vector field is the geodesic spray associated with an affine connection. With the geometric insight gained with this decomposition, we are able to ...

#### Affine connection control systems

(1999)

The affine connection formalism provides a useful framework for the
investigation of a large class of mechanical systems. Mechanical systems
with kinetic energy Lagrangians and possibly with nonholonomic constraints
are ...

#### Group structures in a class of control systems

(1992)

We investigate two classes of control systems, one of Brockett and
one of Murray and Sastry. We are able to show that these two systems
may be formulated in the language of principle fibre bundles. Controllability
of ...