## Search

Now showing items 1-10 of 13

#### 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. ...

#### 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 ...

#### Lifting distributions to tangent and jet bundles

(1998)

We provide two natural ways to lift a distribution from a manifold to its
tangent bundle, and show that they agree if and only if the original
distribution is integrable. The case when the manifold is the total space ...

#### 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 ...

#### 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 ...

#### 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 ...

#### Towards F=ma in a general setting for Lagrangian mechanics

(1998)

By using a suitably general definition of a force, one may geometrically cast
the Euler-Lagrange equations in a ``force balance'' form. The key ingredient
in such a construction is the Euler-Lagrange 2-force which is a ...

#### Variational principles for constrained systems: theory and experiment

(1994)

In this paper we present two methods, the nonholonomic method and the
vakonomic method, for deriving equations of motion for a
mechanical system with constraints. The resulting equations are compared.
Results are also ...

#### 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 ...