A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational
degrees of freedom. The pendulum is acted on by a gravitational force. 3D pendulum …

(cont.) This thesis also presents a new synchronization framework that can be directly
applied to cooperative control of autonomous aerospace vehicles and oscillation …

Pendulum models have been studied as benchmark problems for development of nonlinear
control schemes, as well as reduced-order models for the dynamics analysis of gait, balance …

Surprisingly, aspects of the compelling mystery of “dark matter”—the mysterious,
undiscovered material that supposedly consumes most of a spiral galaxy's mass—are …

We explore the n-body problem, n≥ 3, on a surface of revolution with a general interaction
depending on the pairwise geodesic distance. Using the geometric methods of classical …

The simplest non-collision solutions of the $ N $-body problem are the “relative equilibria”, in
which each body follows a circular orbit around the centre of mass and the shape formed by …

The falling cat and the falling apple of Newton share the same mechanical property, ie,
vanishing angular momentum. We begin by giving a brief review of the falling apple of …

One way to define a sub-Riemannian metric is as the limit of a Riemannian metric. Consider
a Riemannian structure depending on a parameter $ s $ such that its limit defines a sub …

In this paper we show that in the n-body problem with harmonic potential one can find a
continuum of central configurations for n= 3. Moreover we show a counterexample to an …

The question of finding solutions to a given implicit differential equation (IDE) is an important
one, in part because it appears very naturally in several problems in physics, engineering …